مارپیچ

fa-noun

مارپیچ • (mârpič) (plural مارپیچها (mârpič-hâ))

desctree

→ Ottoman Turkish: مارپیچ (marpıç), մարփըչ (marpıç), մարփուչ (marpuç), մարփուճ (marpuc) — Armeno-Turkish
Turkish: marpuç
→ Albanian: markuç
→ Armenian: մարփուճ (marpʻuč), մարփունջ (marpʻunǰ)
→ Bulgarian: марку́ч (markúč)
→ Romanian: marpici

[mɑːɾ.pʰeːt͡ʃ]

[mɑːɾ.pʰeːt͡ʃ]

[mɑːɾ.pʰeːt͡ʃ]

[mɔːɾ.pʰeːt͡ʃ]

[mɒːɹ.pʰiːt͡ʃ]


پیچه

→ Turkish: peçe


bituon

From Proto-Philippine *bituqən, from Proto-Malayo-Polynesian *bituqen, from Proto-Austronesian *bituqen. Compare Tagalog bituin, Tausug bituun.


hyperbolic geometry

en-noun

hyperbolic geometry (countable and uncountable, plural hyperbolic geometries)

The terminology was introduced in 1871 by Felix Klein, who classified some non-Euclidean geometries as hyperbolisch (“hyperbolic”), elliptisch (“elliptical”), and parabolisch (“parabolic”).

parallel postulate
parallel postulate#English

(geometry) A type of geometry that rejects the parallel postulate. Given a straight line L and a point p not on L, more than one straight line can be drawn through p without intersecting L.

(geometry) A non-Euclidean geometry, that features the hyperbola as geodesic, and has constant negative curvature


底邊

/ti²¹⁴⁻²¹ pi̯ɛn⁵⁵/

/tɐi̯³⁵ piːn⁵⁵/

/te⁴¹⁻⁴⁴ pĩ⁴⁴/

/tue⁵³⁻⁴⁴ pĩ⁴⁴/

/ti²¹⁴⁻²¹ pi̯ɛn⁵⁵/

/tɐi̯³⁵ piːn⁵⁵/

/te⁴¹⁻⁴⁴ pĩ⁴⁴/

/tue⁵³⁻⁴⁴ pĩ⁴⁴/


射線

/ʂɤ⁵¹⁻⁵³ ɕi̯ɛn⁵¹/

/sɛː²² siːn³³/

/sia¹¹ sũã²¹³/

/ʂɤ⁵¹⁻⁵³ ɕi̯ɛn⁵¹/

/sɛː²² siːn³³/

/sia¹¹ sũã²¹³/

(geometry) ray; half-line (Classifier: 條／条)


sekskant

sekskant m (definite singular sekskanten, indefinite plural sekskanter, definite plural sekskantene)

sekskanten (definite singular)
sekskanter (indefinite plural)
sekskantene (definite plural)


sekskant

sekskant m (definite singular sekskanten, indefinite plural sekskantar, definite plural sekskantane)

sekskanten (definite singular)
sekskantar (indefinite plural)
sekskantane (definite plural)


oktogon

oktogon m (definite singular oktogonen, indefinite plural oktogoner, definite plural oktogonene)

oktogonen (definite singular)
oktogoner (indefinite plural)
oktogonene (definite plural)


oktogon

oktogon m (definite singular oktogonen, indefinite plural oktogonar, definite plural oktogonane)

oktogonen (definite singular)
oktogonar (indefinite plural)
oktogonane (definite plural)


åttekant

åttekant m (definite singular åttekanten, indefinite plural åttekanter, definite plural åttekantene)

åttekanten (definite singular)
åttekanter (indefinite plural)
åttekantene (definite plural)


åttekant

åttekant m (definite singular åttekanten, indefinite plural åttekantar, definite plural åttekantane)

åttekanten (definite singular)
åttekantar (indefinite plural)
åttekantane (definite plural)


trọng tâm

[t͡ɕawŋ͡m˧˨ʔ təm˧˧]

[ʈawŋ͡m˨˩ʔ təm˧˧]

[ʈɔŋ˨˩ʔ təm˧˧]

[ʈawŋ͡m˨˩˨ təm˧˧]

Trọng tâm của bài học hôm nay là trọng tâm tam giác.

Today's lesson focuses on the centroid of triangles.


trực tâm

[t͡ɕɨk̚˧˨ʔ təm˧˧]

[ʈɨk̚˨˩ʔ təm˧˧]

[ʈɨk̚˨˩˨ təm˧˧]

Sino-Vietnamese word from 直心, composed of 直 (“straight; ortho-”) and 心 (“center”), perhaps a direct calque of a European word for "orthocenter". Unintuitively, this term has nothing to do with the point of intersection of the three đường trung trực (“segment-bisecting lines”) of the three sides of a triangle, the circumcenter, which does not have a common name in Vietnamese.


垂心

/ʈ͡ʂʰu̯eɪ̯³⁵ ɕin⁵⁵/

/sɵy̯²¹ sɐm⁵⁵/

/ʈ͡ʂʰu̯eɪ̯³⁵ ɕin⁵⁵/

/sɵy̯²¹ sɐm⁵⁵/


수심

Sino-Korean word from 垂心, from 垂 (“to dangle; to hang”) + 心 (“heart”)


cirkelafsnit

head

cirkelafsnit n (singular definite cirkelafsnittet, plural indefinite cirkelafsnit)

cirkelafsnittet (definite singular)
cirkelafsnit (indefinite plural)
cirkelafsnit (indefinite nominative singular)
cirkelafsnittet (definite nominative singular)
cirkelafsnit (indefinite nominative plural)
cirkelafsnittene (definite nominative plural)
cirkelafsnits (genitive indefinite singular)
cirkelafsnittets (definite genitive singular)
cirkelafsnits (genitive indefinite plural)
cirkelafsnittenes (definite genitive plural)


cirkeludsnit

cirkeludsnit n (singular definite cirkeludsnittet, plural indefinite cirkeludsnit)

cirkeludsnittet (definite singular)
cirkeludsnit (indefinite plural)
cirkeludsnit (indefinite nominative singular)
cirkeludsnittet (definite nominative singular)
cirkeludsnit (indefinite nominative plural)
cirkeludsnittene (definite nominative plural)
cirkeludsnits (genitive indefinite singular)
cirkeludsnittets (definite genitive singular)
cirkeludsnits (genitive indefinite plural)
cirkeludsnittenes (definite genitive plural)

(geometry) circular sector (area between two radii and circumference)


korde

korde c (singular definite korden, plural indefinite korder)

korden (definite singular)
korder (indefinite plural)
korde (indefinite nominative singular)
korden (definite nominative singular)
korder (indefinite nominative plural)
korderne (definite nominative plural)
kordes (genitive indefinite singular)
kordens (definite genitive singular)
korders (genitive indefinite plural)
kordernes (definite genitive plural)

(geometry) chord; straight line connecting points in a circle's circumference, sometimes excluding the diameter


jordakse

jordakse m (definite singular jordaksen)

(geometry) the Earth's axis, the axis of the Earth.


плӏэнэбзы

плӏэнэбзы • (plˢʼɛnɛbzə)

ady-noun

плӏэнэбзы • (plˢʼɛnɛbzə)

plˢʼɛnɛbzə (romanization)
плӏэнэбзыр (nominative singular)
плӏэнэбзыхэр (nominative plural)
плӏэнэбзым (ergative singular)
плӏэнэбзыхэмэ (ergative plural)
плӏэнэбзыкӏэ (instrumental singular)
плӏэнэбзыкӏэ (instrumental singular)
плӏэнэбзымəkʼɛ) (instrumental singular)
плӏэнэбзымəmkʼɛ) (instrumental singular)
плӏэнэбзыхэкӏэ (instrumental plural)
плӏэнэбзыхэкӏэ (instrumental plural)
плӏэнэбзыхэмɛkʼɛ) (instrumental plural)
плӏэнэбзыхэмɛmkʼɛ) (instrumental plural)
плӏэнэбзыу (invertive singular)
плӏэнэбзыхыу (invertive plural)

ady-decl-noun-table

плӏэнэбзыр (plˢʼɛnɛbzər)

плӏэнэбзыхэр (plˢʼɛnɛbzəxɛr)

плӏэнэбзым (plˢʼɛnɛbzəm)

плӏэнэбзыхэмэ (plˢʼɛnɛbzəxɛmɛ)

плӏэнэбзы(м)кӏэ (plˢʼɛnɛbzə(m)kʼɛ)

плӏэнэбзыхэ(м)кӏэ (plˢʼɛnɛbzəxɛ(m)kʼɛ)

плӏэнэбзыу (plˢʼɛnɛbzəwu)

плӏэнэбзыхыу (plˢʼɛnɛbzəxəwu)


плӏэмыепкъ

head

плӏэмыепкъ • (plˢʼɛməjepq)

ady-noun

плӏэмыепкъ • (plˢʼɛməjepq)

plˢʼɛməjepq (romanization)
плӏэмыепкъэ (indefinite singular)
плӏэмыепкъэхэ (indefinite plural)
плӏэмыепкъэр (nominative singular)
плӏэмыепкъэхэр (nominative plural)
плӏэмыепкъэм (ergative singular)
плӏэмыепкъэхэмэ (ergative plural)
плӏэмыепкъэкӏэ (instrumental singular)
плӏэмыепкъэкӏэ (instrumental singular)
плӏэмыепкъэмɛkʼɛ) (instrumental singular)
плӏэмыепкъэмɛmkʼɛ) (instrumental singular)
плӏэмыепкъэхэкӏэ (instrumental plural)
плӏэмыепкъэхэкӏэ (instrumental plural)
плӏэмыепкъэхэмɛkʼɛ) (instrumental plural)
плӏэмыепкъэхэмɛmkʼɛ) (instrumental plural)
плӏэмыепкъыу (invertive singular)
плӏэмыепкъэхыу (invertive plural)

ady-decl-noun-table

плӏэмыепкъэ (plˢʼɛməjepqɛ)

плӏэмыепкъэхэ (plˢʼɛməjepqɛxɛ)

плӏэмыепкъэр (plˢʼɛməjepqɛr)

плӏэмыепкъэхэр (plˢʼɛməjepqɛxɛr)

плӏэмыепкъэм (plˢʼɛməjepqɛm)

плӏэмыепкъэхэмэ (plˢʼɛməjepqɛxɛmɛ)

плӏэмыепкъэ(м)кӏэ (plˢʼɛməjepqɛ(m)kʼɛ)

плӏэмыепкъэхэ(м)кӏэ (plˢʼɛməjepqɛxɛ(m)kʼɛ)

плӏэмыепкъыу (plˢʼɛməjepqəwu)

плӏэмыепкъэхыу (plˢʼɛməjepqɛxəwu)

From плӏэмый (plˢʼɛməj, “square”) + пкъы (pqə, “body”).


плӏэмый

head

плӏэмый • (plˢʼɛməj)

ady-noun

плӏэмый • (plˢʼɛməj)

plˢʼɛməj (romanization)
плӏэмыйэ (indefinite singular)
плӏэмыйэхэ (indefinite plural)
плӏэмыйэр (nominative singular)
плӏэмыйэхэр (nominative plural)
плӏэмыйэм (ergative singular)
плӏэмыйэхэмэ (ergative plural)
плӏэмыйэкӏэ (instrumental singular)
плӏэмыйэкӏэ (instrumental singular)
плӏэмыйэмɛkʼɛ) (instrumental singular)
плӏэмыйэмɛmkʼɛ) (instrumental singular)
плӏэмыйэхэкӏэ (instrumental plural)
плӏэмыйэхэкӏэ (instrumental plural)
плӏэмыйэхэмɛkʼɛ) (instrumental plural)
плӏэмыйэхэмɛmkʼɛ) (instrumental plural)
плӏэмыйыу (invertive singular)
плӏэмыйэхыу (invertive plural)

ady-decl-noun-table

плӏэмыйэ (plˢʼɛməjɛ)

плӏэмыйэхэ (plˢʼɛməjɛxɛ)

плӏэмыйэр (plˢʼɛməjɛr)

плӏэмыйэхэр (plˢʼɛməjɛxɛr)

плӏэмыйэм (plˢʼɛməjɛm)

плӏэмыйэхэмэ (plˢʼɛməjɛxɛmɛ)

плӏэмыйэ(м)кӏэ (plˢʼɛməjɛ(m)kʼɛ)

плӏэмыйэхэ(м)кӏэ (plˢʼɛməjɛxɛ(m)kʼɛ)

плӏэмыйыу (plˢʼɛməjəwu)

плӏэмыйэхыу (plˢʼɛməjɛxəwu)


зэпэзэдакъ

head

зэпэзэдакъ • (zɛpɛzɛdaq)

ady-noun

зэпэзэдакъ • (zɛpɛzɛdaq)

zɛpɛzɛdaq (romanization)
зэпэзэдакъэ (indefinite singular)
зэпэзэдакъэхэ (indefinite plural)
зэпэзэдакъэр (nominative singular)
зэпэзэдакъэхэр (nominative plural)
зэпэзэдакъэм (ergative singular)
зэпэзэдакъэхэмэ (ergative plural)
зэпэзэдакъэкӏэ (instrumental singular)
зэпэзэдакъэкӏэ (instrumental singular)
зэпэзэдакъэмɛkʼɛ) (instrumental singular)
зэпэзэдакъэмɛmkʼɛ) (instrumental singular)
зэпэзэдакъэхэкӏэ (instrumental plural)
зэпэзэдакъэхэкӏэ (instrumental plural)
зэпэзэдакъэхэмɛkʼɛ) (instrumental plural)
зэпэзэдакъэхэмɛmkʼɛ) (instrumental plural)
зэпэзэдакъыу (invertive singular)
зэпэзэдакъэхыу (invertive plural)

ady-decl-noun-table

зэпэзэдакъэ (zɛpɛzɛdaqɛ)

зэпэзэдакъэхэ (zɛpɛzɛdaqɛxɛ)

зэпэзэдакъэр (zɛpɛzɛdaqɛr)

зэпэзэдакъэхэр (zɛpɛzɛdaqɛxɛr)

зэпэзэдакъэм (zɛpɛzɛdaqɛm)

зэпэзэдакъэхэмэ (zɛpɛzɛdaqɛxɛmɛ)

зэпэзэдакъэ(м)кӏэ (zɛpɛzɛdaqɛ(m)kʼɛ)

зэпэзэдакъэхэ(м)кӏэ (zɛpɛzɛdaqɛxɛ(m)kʼɛ)

зэпэзэдакъыу (zɛpɛzɛdaqəwu)

зэпэзэдакъэхыу (zɛpɛzɛdaqɛxəwu)


щэный

head

щэный • (śɛnəj)

ady-noun

щэный • (śɛnəj)

śɛnəj (romanization)
щэныйэ (indefinite singular)
щэныйэхэ (indefinite plural)
щэныйэр (nominative singular)
щэныйэхэр (nominative plural)
щэныйэм (ergative singular)
щэныйэхэмэ (ergative plural)
щэныйэкӏэ (instrumental singular)
щэныйэкӏэ (instrumental singular)
щэныйэмɛkʼɛ) (instrumental singular)
щэныйэмɛmkʼɛ) (instrumental singular)
щэныйэхэкӏэ (instrumental plural)
щэныйэхэкӏэ (instrumental plural)
щэныйэхэмɛkʼɛ) (instrumental plural)
щэныйэхэмɛmkʼɛ) (instrumental plural)
щэныйыу (invertive singular)
щэныйэхыу (invertive plural)

ady-decl-noun-table

щэныйэ (śɛnəjɛ)

щэныйэхэ (śɛnəjɛxɛ)

щэныйэр (śɛnəjɛr)

щэныйэхэр (śɛnəjɛxɛr)

щэныйэм (śɛnəjɛm)

щэныйэхэмэ (śɛnəjɛxɛmɛ)

щэныйэ(м)кӏэ (śɛnəjɛ(m)kʼɛ)

щэныйэхэ(м)кӏэ (śɛnəjɛxɛ(m)kʼɛ)

щэныйыу (śɛnəjəwu)

щэныйэхыу (śɛnəjɛxəwu)


paral·lelepípede

ca-noun

paral·lelepípede m (plural paral·lelepípedes)


tesseractic

LL-Q1860 (eng)-Flame, not lame-tesseractic.wav

(geometry) Relating to a tesseract; relating to four-dimensional space or to a 4-polytope


trisector

LL-Q1860 (eng)-Flame, not lame-trisector.wav

(geometry) A line or curve that trisects something.


spinode

LL-Q1860 (eng)-Flame, not lame-spinode.wav


정사각형

jeongsagakhyeong (romanization)
正四角形 (hanja)

[ˈt͡ɕɘ(ː)ŋsʰa̠ɡa̠cçʌ̹ŋ]


Houk

From Old Frisian hōk, from Proto-West Germanic *hōk, from Proto-Germanic *hōkaz. Cognates include West Frisian hoek and Dutch hoek.


橢圓

CJKV/code

Sino-Xenic (橢圓):
* → Japanese: 楕(だ)円(えん) (daen)
* → Korean: 타원(楕圓) (tawon)

/tʰu̯ɔ²¹⁴⁻²¹ ɥɛn³⁵/

/tʰu̯ɔ²¹⁴⁻²¹ ɥɑɻ³⁵/

/tʰɔː¹³ jyːn²¹/

/tʰuo³³⁻²¹ uoŋ⁵³/

/tʰo⁴¹⁻⁵⁵⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ¹³/

/tʰo⁵²⁻³⁵ ĩ⁵⁵/

/tʰu̯ɔ²¹⁴⁻²¹ ɥɛn³⁵/

/tʰu̯ɔ²¹⁴⁻²¹ ɥɑɻ³⁵/

/tʰɔː¹³ jyːn²¹/

/tʰuo³³⁻²¹ uoŋ⁵³/

/tʰo⁴¹⁻⁵⁵⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ²⁴/

/tʰo⁵³⁻⁴⁴ ĩ¹³/

/tʰo⁵²⁻³⁵ ĩ⁵⁵/


starlikeness

LL-Q1860 (eng)-Flame, not lame-starlikeness.wav

(geometry) The property of being starlike.


rhombitrihexagonal

LL-Q1860 (eng)-Flame, not lame-rhombitrihexagonal.wav

(geometry) Relating to a semiregular tiling of the Euclidean plane with one triangle, two squares, and one hexagon on each vertex.


isotoxal

LL-Q1860 (eng)-Flame, not lame-isotoxal.wav

(geometry, of a polytope or tiling) That has symmetries which act transitively on its edges.

edge-symmetric

having symmetries that act transitively on its edges


linea retta

From linea (“line”) + retta (“straight”).


acylindrical

LL-Q1860 (eng)-Flame, not lame-acylindrical.wav


агол

mk-noun

агол • (agol) m (plural агли, diminutive аголен)

agol (romanization)
агли (plural)
аголен (diminutive)
агол (indefinite singular)
агли (indefinite plural)
аголот (definite singular unspecified)
аглите (definite plural unspecified)
аголов (definite proximal singular)
агливе (definite plural proximal)
аголон (definite distal singular)
аглине (definite distal plural)
аголу (singular vocative)
агли (plural vocative)
агола (count-form plural)

Inherited from Proto-Slavic *ǫgъlъ, from Proto-Balto-Slavic *ángulas, from Proto-Indo-European *h₂éngulos.


плоштина

плоштина • (ploština) f

ploština (romanization)
плоштина (indefinite singular)
плоштини (indefinite plural)
плоштината (definite singular unspecified)
плоштините (definite plural unspecified)
плоштинава (definite proximal singular)
плоштиниве (definite plural proximal)
плоштинана (definite distal singular)
плоштинине (definite distal plural)
плоштино (singular vocative)
плоштини (plural vocative)


многуаголник

многуаголници

многуаголник • (mnoguagolnik) m (plural многуаголници, relational adjective многуаголен)

mnoguagolnik (romanization)
многуаголници (plural)
многуаголен (adjective relational)
многуаголник (indefinite singular)
многуаголници (indefinite plural)
многуаголникот (definite singular unspecified)
многуаголниците (definite plural unspecified)
многуаголников (definite proximal singular)
многуаголнициве (definite plural proximal)
многуаголникон (definite distal singular)
многуаголницине (definite distal plural)
многуаголнику (singular vocative)
многуаголници (plural vocative)
многуаголника (count-form plural)

mk-decl-noun-m

многуаголниц

mk-decl-noun-table

многуаголник

многуаголникот

многуаголников

многуаголникон

многуаголнику

многуаголникје

многуаголници

многуаголниците

многуаголнициве

многуаголницине

многуаголници

многуаголника

мно гу а гол ник

By surface analysis, многу (mnogu, “many”) + агол (agol, “angle, corner”) + -ник (-nik).


петаголник

mk-noun

петаголник • (petagolnik) m (plural петаголници, relational adjective петаголен)

petagolnik (romanization)
петаголници (plural)
петаголен (adjective relational)
петаголник (indefinite singular)
петаголници (indefinite plural)
петаголникот (definite singular unspecified)
петаголниците (definite plural unspecified)
петаголников (definite proximal singular)
петаголнициве (definite plural proximal)
петаголникон (definite distal singular)
петаголницине (definite distal plural)
петаголнику (singular vocative)
петаголници (plural vocative)
петаголника (count-form plural)

mk-decl-noun-table

петаголникот

петаголников

петаголникон

петаголникје

петаголниците

петаголнициве

петаголницине

By surface analysis, пет (pet, “five”) + агол (agol, “angle, corner”) + -ник (-nik).


шестаголник

mk-noun

шестаголници

шестаголник • (šestagolnik) m (plural шестаголници, relational adjective шестаголен)

šestagolnik (romanization)
шестаголници (plural)
шестаголен (adjective relational)
шестаголник (indefinite singular)
шестаголници (indefinite plural)
шестаголникот (definite singular unspecified)
шестаголниците (definite plural unspecified)
шестаголников (definite proximal singular)
шестаголнициве (definite plural proximal)
шестаголникон (definite distal singular)
шестаголницине (definite distal plural)
шестаголнику (singular vocative)
шестаголници (plural vocative)
шестаголника (count-form plural)

mk-decl-noun-table

шестаголникот

шестаголников

шестаголникон

шестаголнику

шестаголникје

шестаголници

шестаголниците

шестаголнициве

шестаголницине

шестаголници

шестаголника

By surface analysis, шест (šest, “six”) + агол (agol, “angle, corner”) + -ник (-nik).


седумаголник

mk-noun

седумаголници

седумаголник • (sedumagolnik) m (plural седумаголници, relational adjective седумаголен)

sedumagolnik (romanization)
седумаголници (plural)
седумаголен (adjective relational)
седумаголник (indefinite singular)
седумаголници (indefinite plural)
седумаголникот (definite singular unspecified)
седумаголниците (definite plural unspecified)
седумаголников (definite proximal singular)
седумаголнициве (definite plural proximal)
седумаголникон (definite distal singular)
седумаголницине (definite distal plural)
седумаголнику (singular vocative)
седумаголници (plural vocative)
седумаголника (count-form plural)

mk-decl-noun-m

седумаголниц

mk-decl-noun-table

седумаголник

седумаголникот

седумаголников

седумаголникон

седумаголнику

седумаголникје

седумаголници

седумаголниците

седумаголнициве

седумаголницине

седумаголници

седумаголника

By surface analysis, седум (sedum, “seven”) + агол (agol, “angle, corner”) + -ник (-nik).


осумаголник

mk-noun

осумаголници

осумаголник • (osumagolnik) m (plural осумаголници, relational adjective осумаголен)

osumagolnik (romanization)
осумаголници (plural)
осумаголен (adjective relational)
осумаголник (indefinite singular)
осумаголници (indefinite plural)
осумаголникот (definite singular unspecified)
осумаголниците (definite plural unspecified)
осумаголников (definite proximal singular)
осумаголнициве (definite plural proximal)
осумаголникон (definite distal singular)
осумаголницине (definite distal plural)
осумаголнику (singular vocative)
осумаголници (plural vocative)
осумаголника (count-form plural)

mk-decl-noun-table

осумаголникот

осумаголников

осумаголникон

осумаголнику

осумаголникје

осумаголници

осумаголниците

осумаголнициве

осумаголницине

осумаголници

осумаголника

By surface analysis, осум (osum, “eight”) + агол (agol, “angle, corner”) + -ник (-nik).


деветаголник

mk-noun

деветаголници

деветаголник • (devetagolnik) m (plural деветаголници, relational adjective деветаголен)

devetagolnik (romanization)
деветаголници (plural)
деветаголен (adjective relational)
деветаголник (indefinite singular)
деветаголници (indefinite plural)
деветаголникот (definite singular unspecified)
деветаголниците (definite plural unspecified)
деветаголников (definite proximal singular)
деветаголнициве (definite plural proximal)
деветаголникон (definite distal singular)
деветаголницине (definite distal plural)
деветаголнику (singular vocative)
деветаголници (plural vocative)
деветаголника (count-form plural)

mk-decl-noun-m

деветаголниц

mk-decl-noun-table

деветаголник

деветаголникот

деветаголников

деветаголникон

деветаголнику

деветаголникје

деветаголници

деветаголниците

деветаголнициве

деветаголницине

деветаголници

деветаголника

By surface analysis, девет (devet, “nine”) + агол (agol, “angle, corner”) + -ник (-nik).


десетаголник

mk-noun

десетаголници

десетаголник • (desetagolnik) m (plural десетаголници, relational adjective десетаголен)

desetagolnik (romanization)
десетаголници (plural)
десетаголен (adjective relational)
десетаголник (indefinite singular)
десетаголници (indefinite plural)
десетаголникот (definite singular unspecified)
десетаголниците (definite plural unspecified)
десетаголников (definite proximal singular)
десетаголнициве (definite plural proximal)
десетаголникон (definite distal singular)
десетаголницине (definite distal plural)
десетаголнику (singular vocative)
десетаголници (plural vocative)
десетаголника (count-form plural)

mk-decl-noun-m

десетаголниц

mk-decl-noun-table

десетаголник

десетаголникот

десетаголников

десетаголникон

десетаголнику

десетаголникје

десетаголници

десетаголниците

десетаголнициве

десетаголницине

десетаголници

десетаголника

By surface analysis, десет (deset, “ten”) + агол (agol, “angle, corner”) + -ник (-nik).


Inkreis

de-noun

Inkreis m (strong, genitive Inkreises, plural Inkreise)

Inkreises (genitive)
Inkreise (plural)
Inkreis (nominative singular)
Inkreise (definite nominative plural)
Inkreises (genitive singular)
Inkreise (definite genitive plural)
Inkreis (dative singular)
Inkreise (dative singular)
Inkreisen (dative definite plural)
Inkreis (accusative singular)
Inkreise (accusative definite plural)

[ˈɪnˌkʁaɪ̯s]


Inkreisradius

Inkreisradius m (strong, genitive Inkreisradius, plural Inkreisradien)

Inkreisradius (genitive)
Inkreisradien (plural)
Inkreisradius (nominative singular)
Inkreisradien (definite nominative plural)
Inkreisradius (genitive singular)
Inkreisradien (definite genitive plural)
Inkreisradius (dative singular)
Inkreisradien (dative definite plural)
Inkreisradius (accusative singular)
Inkreisradien (accusative definite plural)

[ˈɪnˌkʁaɪ̯sˌʁaːdi̯ʊs]

From Inkreis (“incircle”) + Radius (“radius”).


остар

mk-adj

остар • (ostar) (comparative поостар, superlative најостар, diminutive остричок, abstract noun острина)

ostar (romanization)
поостар (comparative)
најостар (superlative)
остричок (diminutive)
острина (abstract-noun)
остар (indefinite masculine)
остра (feminine indefinite)
остро (indefinite neuter)
остри (indefinite plural)
остриот (definite masculine unspecified)
острата (definite feminine unspecified)
острото (definite neuter unspecified)
острите (definite plural unspecified)
остриов (definite masculine proximal)
острава (definite feminine proximal)
острово (definite neuter proximal)
остриве (definite plural proximal)
острион (definite distal masculine)
острана (definite distal feminine)
остроно (definite distal neuter)
острине (definite distal plural)
поостар (indefinite masculine)
поостра (feminine indefinite)
поостро (indefinite neuter)
поостри (indefinite plural)
поостриот (definite masculine unspecified)
поострата (definite feminine unspecified)
поострото (definite neuter unspecified)
поострите (definite plural unspecified)
поостриов (definite masculine proximal)
поострава (definite feminine proximal)
поострово (definite neuter proximal)
поостриве (definite plural proximal)
поострион (definite distal masculine)
поострана (definite distal feminine)
поостроно (definite distal neuter)
поострине (definite distal plural)
најостар (indefinite masculine)
најостра (feminine indefinite)
најостро (indefinite neuter)
најостри (indefinite plural)
најостриот (definite masculine unspecified)
најострата (definite feminine unspecified)
најострото (definite neuter unspecified)
најострите (definite plural unspecified)
најостриов (definite masculine proximal)
најострава (definite feminine proximal)
најострово (definite neuter proximal)
најостриве (definite plural proximal)
најострион (definite distal masculine)
најострана (definite distal feminine)
најостроно (definite distal neuter)
најострине (definite distal plural)


geometria não-euclidiana

pt-noun

geometria não-euclidiana f (plural geometrias não-euclidianas)

non-Euclidean geometry
non-Euclidean geometry

(geometry) non-Euclidean geometry (any system of geometry not based on the set of axioms of Euclidean geometry)


scalebound

LL-Q1860 (eng)-Flame, not lame-scalebound.wav

From scale + bound, coined by the mathematician Benoit Mandelbrot in a 1981 paper.

(geometry) Of an object: for which characteristic elements of scale, such as length and width, are few in number and each with a clearly distinct size.


heptaedro

[ˌɛ.ptɐˈɛ.ðɾu]

(geometry) heptahedron (polyhedron with seven faces)


nauhcampa nacaceh machiyotl

nāuhcāmpa nacaceh machiyōtl (canonical)
nauhcampanacacemachiotl (alternative)

From nāuhcāmpa (“in four directions”) + nacaceh (“cornered object”) + machiyōtl (“model, figure”).

compound

Figura de quatro angulos. nauhcampanacacemachiotl. y aſ / ſi delos de mas`

1555, Alonso de Molina, Aqui comienca vn vocabulario en la lengua castellana y mexicana, f. 123v:

A shape with four angles. nauhcampanacacemachiotl. and likewise for the rest of them.

(geometry) (it is) a plane figure or object with four straight angles; a square or rectangle.


vuông

head

𣃱, 𣄇, 𣄖, 𩖫, 𪯵, 𪯾

vi-adj

𣃱, 𣄇, 𣄖, 𩖫, 𪯵, 𪯾

𣃱 (CJK)
𣄇 (CJK)
𣄖 (CJK)
𩖫 (CJK)
𪯵 (CJK)
𪯾 (CJK)

LL-Q9199 (vie)-Jessica Nguyen (Pamputt)-vuông.wav

Non-Sino-Vietnamese reading of Chinese 方 (“square”, SV: phương).

der

SV: <i class="Latn mention" lang="vi">phương</i>

vi-etym-sino

góc vuông

tam giác vuông

Đường thẳng d vuông góc với đường thẳng t.


sextantal

LL-Q1860 (eng)-Flame, not lame-sextantal.wav


बहुभुज

bahubhuj (romanization)
बहुभुज (direct singular)
बहुभुज (direct plural)
बहुभुज (oblique singular)
बहुभुजों (oblique plural)
बहुभुज (singular vocative)
बहुभुजो (plural vocative)

/bə.ɦʊ.bʱʊd͡ʒ/

[bɔ.ɦɔ.bʱʊd͡ʒ]

From बहु (bahu, “many”) + भुज (bhuj, “bending, curve”).

compound

polygon (a two-dimensional shape made with only straight lines and non-overlapping sides)


ピタゴラスの定理

ja-noun

^ピタゴラス の ていり

ピタゴラスの定理 (canonical)
Pitagorasu no teiri (romanization)

ピタゴラス (Pitagorasu, “Pythagoras”) + の (no, “'s”) + 定理 (teiri, “theorem”)

com

(geometry, functional analysis) the Pythagorean theorem


आस

→ Gujarati: આંસ (ā̃sa)

Etymology tree
Proto-Indo-European *h₂eǵ-?
Proto-Indo-European *-os?
Proto-Indo-European *h₂eḱs-
Proto-Indo-European *-os
Proto-Indo-Iranian *Háćšas
Sanskrit अक्ष॑ (ákṣa)
Prakrit 𑀅𑀓𑁆𑀔 (akkha)
Old Marathi 𑘁𑘽𑘏 (āṃkha)
Marathi आस (ās)
Inherited from Old Marathi *𑘁𑘽𑘭 (*āṃsa) (see 𑘁𑘽𑘏 (āṃkha)), from Prakrit *𑀅𑀘𑁆𑀙 (*accha) (see 𑀅𑀓𑁆𑀔 (akkha)), from Sanskrit अक्ष॑ (ákṣa). Doublet of अक्ष (akṣa).


रेखागणित

hi-noun

रेखागणित • (rekhāgaṇit) m

rekhāgaṇit (romanization)
रेखागणित (direct singular)
रेखागणित (direct plural)
रेखागणित (oblique singular)
रेखागणितों (oblique plural)
रेखागणित (singular vocative)
रेखागणितो (plural vocative)

hi-ndecl

//रेखाग*णित<M>

/ɾeː.kʰɑː.ɡə.ɳɪt̪/

[ɾeː.kʰäː.ɡɐ.ɳɪt̪]

Learned borrowing from Sanskrit रेखागणित (rekhāgaṇita), equivalent to रेखा (rekhā, “line”) + गणित (gaṇit, “math”).


रेखागणित

head

रेखागणित • (rekhāgṇit) n

mr-noun

रेखागणित • (rekhāgṇit) n

rekhāgṇit (romanization)
रेखागणित
रेखागणिते
रेखागणितं
रेखागणिता
रेखागणितां-
रेखागणिताला
रेखागणितांना
रेखागणिताने (ergative)
रेखागणितानं (ergative)
रेखागणितांनी (ergative)
रेखागणिताशी (instrumental)
रेखागणितांशी (instrumental)
Locative Note: -त  is a postposition.
रेखागणिताचा
रेखागणिताचे
रेखागणिताची
रेखागणिताच्या
रेखागणिताचं
रेखागणितांचा
रेखागणितांचे
रेखागणितांची
रेखागणितांच्या
रेखागणितांचं
रेखागणितांच्या

mr-decl-noun

neut cons-stem

mr-decl-noun/link

रेखागणितांना

रेखागणितांनी

रेखागणितांशी

रेखागणितांनो

रेखागणिताच्या

रेखागणिताच्या

रेखागणितांचा

रेखागणितांचे

रेखागणितांची

रेखागणितांच्या

रेखागणितांचे

रेखागणितांचं

रेखागणितांची

रेखागणितांच्या


रेखागणित

rekhāgaṇita (romanization)
रेखागणितम् (nominative singular)
रेखागणिते (dual nominative)
रेखागणितानि (nominative plural)
रेखागणिता1 (nominative plural)
रेखागणितम् (accusative singular)
रेखागणिते (accusative dual)
रेखागणितानि (accusative plural)
रेखागणिता1 (accusative plural)
रेखागणितेन (instrumental singular)
रेखागणिताभ्याम् (dual instrumental)
रेखागणितैः (instrumental plural)
रेखागणितेभिः1 (instrumental plural)
रेखागणिताय (dative singular)
रेखागणिताभ्याम् (dative dual)
रेखागणितेभ्यः (dative plural)
रेखागणितात् (ablative singular)
रेखागणिताभ्याम् (ablative dual)
रेखागणितेभ्यः (ablative plural)
रेखागणितस्य (genitive singular)
रेखागणितयोः (dual genitive)
रेखागणितानाम् (genitive plural)
रेखागणिते (locative singular)
रेखागणितयोः (dual locative)
रेखागणितेषु (locative plural)
रेखागणित (singular vocative)
रेखागणिते (dual vocative)
रेखागणितानि (plural vocative)
रेखागणिता1 (plural vocative)

→ Hindi: रेखागणित (rekhāgṇit) (learned)

→ Khmer: រេខាគណិត (reikhaakĕəʼnət)

desc

→ Lao: ເຣຂາຄະນິດ (rē khā kha nit), ເລຂາຄະນິດ (lē khā kha nit)

→ Marathi: रेखागणित (rekhāgṇit) (learned)

→ Thai: เรขาคณิต (ree-kǎa-ká-nít)

/ɾeː.kʰɑː.ɡɐ.ɳi.t̪ɐ/

रेखा (rekhā, “line”) + गणित (gaṇita, “math”).


geodetisk

head

geodetisk (neuter singular geodetisk, definite singular and plural geodetiske)

geodetisk (neuter singular)
geodetiske (definite plural singular)


uillinn istigh

uillinn istigh f (genitive singular uillinne istigh, nominative plural uilleannacha istigh)

uillinne istigh (genitive singular)
uilleannacha istigh (nominative plural)
uillinn istigh (indefinite nominative singular)
uilleannacha istigh (indefinite nominative plural)
a uillinn istigh (indefinite singular vocative)
a uilleannacha istigh (indefinite plural vocative)
uillinne istigh (genitive indefinite singular)
uilleannacha istigh (genitive indefinite plural)
uillinn istigh (dative indefinite singular)
uilleannacha istigh (dative indefinite plural)
an uillinn istigh (definite nominative singular)
na huilleannacha istigh (definite nominative plural)
na huillinne istigh (definite genitive singular)
na n-uilleannacha istigh (definite genitive plural)
leis an uillinn istigh (dative definite singular)
don uillinn istigh (dative definite singular)
leis na huilleannacha istigh (dative definite plural)
uillinn istigh
n-uillinn istigh
huillinn istigh


ज्यामिति

hi-noun

ज्यामिति • (jyāmiti) f (Urdu spelling جیامِیتی)

jyāmiti (romanization)
جیامِیتی (Urdu)
ज्यामिति (direct singular)
ज्यामितियाँ (direct plural)
ज्यामिति (oblique singular)
ज्यामितियों (oblique plural)
ज्यामिति (singular vocative)
ज्यामितियो (plural vocative)

Phono-semantic matching of English geometry; Sanskritic formation from ज्या (jyā, “chord”) + मिति (miti, “measurement”). Compare Bengali জ্যামিতি (jêmiti), Telugu జ్యామితి (jyāmiti).

sa-com

अंकगणित के अतिरिक्त बीजगणित[,] ज्यामिति और त्रिकोणमिति के क्षेत्र में भी भारतीय ज्योतिषियों का ज्ञान पर्याप्त विकसित एवं प्रौढ़ था।

1969, गोविन्द राम शर्मा [govind rām śarmā], संस्कृत-साहित्य की प्रमुख प्रवृत्तियाँ [sanskŕt-sāhitya kī pramukh pravŕttiyā̃], page 16:

Apart from arithmetic, Indian astrologers had well-developed and advanced knowledge of algebra, geometry and trigonometry.


ज्यामिति

head

ज्यामिति • (jyāmiti) f

mr-noun

ज्यामिति • (jyāmiti) f

jyāmiti (romanization)
ज्यामिती
ज्यामित्या
ज्यामित्यां-
ज्यामितीला
ज्यामित्यांना
ज्यामितीने (ergative)
ज्यामितीनं (ergative)
ज्यामित्यांनी (ergative)
ज्यामितीशी (instrumental)
ज्यामित्यांशी (instrumental)
Locative Note: -त  is a postposition.
ज्यामितीचा
ज्यामितीचे
ज्यामितीची
ज्यामितीच्या
ज्यामितीचं
ज्यामित्यांचा
ज्यामित्यांचे
ज्यामित्यांची
ज्यामित्यांच्या
ज्यामित्यांचं
ज्यामित्यांच्या

mr-decl-noun

fem ī-stem

mr-decl-noun/link

ज्यामित्यां-

ज्यामित्यांना

ज्यामित्यांनी

ज्यामित्यांशी

ज्यामित्यांत

ज्यामित्यांनो

ज्यामितीच्या

ज्यामितीच्या

ज्यामित्यांचा

ज्यामित्यांचे

ज्यामित्यांची

ज्यामित्यांच्या

ज्यामित्यांचे

ज्यामित्यांचं

ज्यामित्यांची

ज्यामित्यांच्या


องศา

/ʔoŋ˧.saː˩˩˦/

From Sanskrit अंश (aṃśa, “fraction; part; portion; etc”). Cognate with Khmer អង្សា (ʼɑɑʼɑngsaa).

der

(geometry, geology, astronomy) degree: unit of angle, equal to ¹⁄₃₆₀ of a circle.


apeirogonal

LL-Q1860 (eng)-Flame, not lame-apeirogonal.wav

(geometry) Having the form of an apeirogon.


จัตุรัส

th-noun

จัตุรัส • (jàt-dtù-ràt)


מחומש

he-noun

מְחֻמָּשִׁים

מחומש / מְחֻמָּשׁ • (m'khumásh) m (plural indefinite מחומשים / מְחֻמָּשִׁים)

מְחֻמָּשׁ (canonical)
m'khumásh (romanization)
מחומשים (indefinite plural)
מְחֻמָּשִׁים (indefinite plural)


góc bẹt

[ɣawk͡p̚˧˦ ʔɓɛt̚˧˨ʔ]

[ɣawk͡p̚˦˧˥ ʔɓɛt̚˨˩ʔ]

[ɣawk͡p̚˦˥ ʔɓɛk̚˨˩˨]


góc phụ nhau

[ɣawk͡p̚˧˦ fu˧˨ʔ ɲaw˧˧]

[ɣawk͡p̚˦˧˥ fʊw˨˩ʔ ɲaw˧˧]

[ɣawk͡p̚˦˥ fʊw˨˩˨ ɲa(ː)w˧˧]


góc kề nhau

[ɣawk͡p̚˧˦ ke˨˩ ɲaw˧˧]

[ɣawk͡p̚˦˧˥ kej˦˩ ɲaw˧˧]


góc bù nhau

[ɣawk͡p̚˧˦ ʔɓu˨˩ ɲaw˧˧]

[ɣawk͡p̚˦˧˥ ʔɓʊw˦˩ ɲaw˧˧]

[ɣawk͡p̚˦˥ ʔɓʊw˨˩ ɲa(ː)w˧˧]


góc đối đỉnh

head

góc đối đỉnh

vi-noun

góc đối đỉnh

[ɣawk͡p̚˧˦ ʔɗoj˧˦ ʔɗïŋ˧˩]

[ɣawk͡p̚˦˧˥ ʔɗoj˨˩˦ ʔɗɨn˧˨]

[ɣawk͡p̚˦˥ ʔɗoj˦˥ ʔɗɨn˨˩˦]

(geometry) vertical angles; opposite angles


đường tròn nội tiếp

[ʔɗɨəŋ˨˩ t͡ɕɔn˨˩ noj˧˨ʔ tiəp̚˧˦]

[ʔɗɨəŋ˦˩ ʈɔŋ˦˩ noj˨˩ʔ tiəp̚˦˧˥]

[ʔɗɨəŋ˨˩ ʈɔŋ˨˩ noj˨˩˨ tip̚˦˥]

Compare Chinese 內接圓 /内接圆 (nội tiếp viên), Japanese 内接円 (naisetsuen), Korean 내접원 (naejeobwon).


đường tròn bàng tiếp

[ʔɗɨəŋ˨˩ t͡ɕɔn˨˩ ʔɓaːŋ˨˩ tiəp̚˧˦]

[ʔɗɨəŋ˦˩ ʈɔŋ˦˩ ʔɓaːŋ˦˩ tiəp̚˦˧˥]

[ʔɗɨəŋ˨˩ ʈɔŋ˨˩ ʔɓaːŋ˨˩ tip̚˦˥]

Compare Japanese 傍接円 (bōsetsuen, bàng tiếp viên), Korean 방접원 (bangjeobwon).


đường tròn ngoại tiếp

[ʔɗɨəŋ˨˩ t͡ɕɔn˨˩ ŋwaːj˧˨ʔ tiəp̚˧˦]

[ʔɗɨəŋ˦˩ ʈɔŋ˦˩ ŋwaːj˨˩ʔ tiəp̚˦˧˥]

[ʔɗɨəŋ˨˩ ʈɔŋ˨˩ ŋwaːj˨˩˨ tip̚˦˥]

Compare Chinese 外接圓 /外接圆 (ngoại tiếp viên), Japanese 外接円 (gaisetsuen), Korean 외접원 (oejeobwon).


circumscribed circle

en-noun

circumscribed circle (plural circumscribed circles)


外接圓

/waɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/ŋɔːi̯²² t͡siːp̚³ jyːn²¹/

/waɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/ŋɔːi̯²² t͡siːp̚³ jyːn²¹/


외접원

[ˈø̞(ː)d͡ʑʌ̹bwʌ̹n]

Sino-Korean word from 外接圓, from 外 (“outside”) + 接 (“to connect”) + 圓 (“circle”)


外接円

ja-noun

外(がい)接(せつ)円(えん) • (gaisetsuen) ^(←ぐわいせつゑん (gwaisetwen)?)

外接円 (canonical)
gaisetsuen (romanization)
gwaisetwen (romanization)
ぐわいせつゑん (hiragana historical)

[ɡa̠ise̞t͡sɨẽ̞ɴ]


内接円

内(ない)接(せつ)円(えん) • (naisetsuen) ^(←ないせつゑん (naisetwen)?)

内接円 (canonical)
naisetsuen (romanization)
naisetwen (romanization)
ないせつゑん (hiragana historical)

ja:三角形の内接円と傍接円 ja:内接円


傍接円

傍(ぼう)接(せつ)円(えん) • (bōsetsuen) ^(←ばうせつゑん (bausetwen)?)

傍接円 (canonical)
bōsetsuen (romanization)
bausetwen (romanization)
ばうせつゑん (hiragana historical)

[bo̞ːse̞t͡sɨẽ̞ɴ]

ja:三角形の内接円と傍接円


inscribed circle

en-noun

inscribed circle (plural inscribed circles)


傍心

ja-noun

傍(ぼう)心(しん) • (bōshin) ^(←ばうしん (bausin)?)

傍心 (canonical)
bōshin (romanization)
bausin (romanization)
ばうしん (hiragana historical)


內接圓

/neɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/nɔːi̯²² t͡siːp̚³ jyːn²¹/

/neɪ̯⁵¹ t͡ɕi̯ɛ⁵⁵ ɥɛn³⁵/

/nɔːi̯²² t͡siːp̚³ jyːn²¹/

(geometry) Alternative name for 內切圓／内切圆 (nèiqiēyuán, “incircle”).


내접원

[ˈnɛ(ː)d͡ʑʌ̹bwʌ̹n]

Sino-Korean word from 內接圓, from 內 (“inside”) + 接 (“to connect”) + 圓 (“circle”)


방접원

[pa̠ŋd͡ʑʌ̹bwʌ̹n]

Sino-Korean word from 傍接圓, from 傍 (“side”) + 接 (“to connect”) + 圓 (“circle”)


방심

Sino-Korean word from 傍心, from 傍 (“side”) + 心 (“center”)


외심

[ˈø̞(ː)ɕʰim]

Sino-Korean word from 外心, from 外 (“outside”) + 心 (“center”)


point of tangency

en-noun

point of tangency (plural points of tangency)

(geometry) The point where a tangent line and its curve meet

切點 /切点

the point where a tangent line and its curve meet


접선

[t͡ɕʌ̹ps͈ʌ̹n]

Sino-Korean word from 接線, from 接 (“to connect”) + 線 (“line”)


Coxeter group

Named for British-born Canadian mathematician H. S. M. Coxeter (1907–2003).

We may ask in general which Coxeter groups arise as subgroups of a given Coxeter group. This question is of course far too general. However, there are Coxeter groups which arise canonically as subgroups of a given Coxeter group.

1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. de Clerck, editors, Finite Geometries and Combinatorics, page 277:

The above definitions, of Cayley graph, reflection, wall, half-space, folding, Bruhat order, etc., work for any Coxeter group.

2007, Michael B. Smythe, Julian Webster, “12: Discrete Spatial Models”, in Marco Aiello, Ian Pratt-Hartmann, Johan van Benthem, editors, Handbook of Spatial Logics, page 795:

The problem of classifying all reflective lattices of given rank is also of interest in its own right from the perspectives of Coxeter groups and arithmetic subgroups of O(n,1).

2012, Daniel Allcock, “The Reflective Lorentzian Lattices of Rank 3”, in Memoirs of the American Mathematical Society, number 1033, page vii:

(mathematics, geometry, group theory) Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.

Coxeter group
Harold Scott MacDonald Coxeter


vertex figure

1970, Harold Scott Macdonald Coxeter, Twisted Honeycombs, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics: Number 4, American Mathematical Society, page 14,
Thus the vertex figure of a polygon is the line-segment whose end-points are the vertex figures of the two edges at one vertex, the vertex figure of a polyhedron or tessellation {p, q} is the polygon {q} whose edges are the vertex figures of the q faces at one vertex, and the analogous "vertex figure" of the honeycomb of cubes (§1) is the polyhedron whose faces are the vertex figures of the eight cubic cells that come together at one vertex.

Now try to see which of these vertex figures cannot be continued to give a semiregular tiling of the whole plane.

1987, A. Gardiner, Mathematical Puzzling, Dover, published 1999, page 137:

At each vertex of a tessellation, the vertex figure is the polygon formed by joining in order the mid-points of all edges incident with the vertex. A tessellation of a surface for which all the participating polygons and vertex figures are regular and equal is termed a regular tessellation.

2004, Michael F. Worboys, Matt Duckham, GIS: A Computing Perspective, 2nd edition, page 188:

(geometry) The figure exposed when a corner of a polyhedron or polytope is sliced off.


ἰσοσκελής

ἰσοσκελής • (isoskelḗs) m or f (neuter ἰσοσκελές); third declension

isoskelḗs (romanization)
ἰσοσκελές (neuter)
ἰσοσκελής (feminine masculine nominative singular)
ἰσοσκελές (neuter nominative singular)
ἰσοσκελεῖ (dual feminine masculine nominative)
ἰσοσκελεῖ (dual neuter nominative)
ἰσοσκελεῖς (feminine masculine nominative plural)
ἰσοσκελῆ (neuter nominative plural)
ἰσοσκελοῦς (feminine genitive masculine singular)
ἰσοσκελοῦς (genitive neuter singular)
ἰσοσκελοῖν (dual feminine genitive masculine)
ἰσοσκελοῖν (dual genitive neuter)
ἰσοσκελῶν (feminine genitive masculine plural)
ἰσοσκελῶν (genitive neuter plural)
ἰσοσκελεῖ (dative feminine masculine singular)
ἰσοσκελεῖ (dative neuter singular)
ἰσοσκελοῖν (dative dual feminine masculine)
ἰσοσκελοῖν (dative dual neuter)
ἰσοσκελέσῐ (dative feminine masculine plural)
ἰσοσκελέσῐν (dative feminine masculine plural)
isoskelésĭ (dative feminine masculine plural)
isoskelésĭn (dative feminine masculine plural)
ἰσοσκελέσῐ (dative neuter plural)
ἰσοσκελέσῐν (dative neuter plural)
isoskelésĭ (dative neuter plural)
isoskelésĭn (dative neuter plural)
ἰσοσκελῆ (accusative feminine masculine singular)
ἰσοσκελές (accusative neuter singular)
ἰσοσκελεῖ (accusative dual feminine masculine)
ἰσοσκελεῖ (accusative dual neuter)
ἰσοσκελεῖς (accusative feminine masculine plural)
ἰσοσκελῆ (accusative neuter plural)
ἰσοσκελές (feminine masculine singular vocative)
ἰσοσκελές (neuter singular vocative)
ἰσοσκελεῖ (dual feminine masculine vocative)
ἰσοσκελεῖ (dual neuter vocative)
ἰσοσκελεῖς (feminine masculine plural vocative)
ἰσοσκελῆ (neuter plural vocative)
ἰσοσκελῶς (adverbial feminine masculine neuter)
ἰσοσκελέστερος (comparative feminine masculine neuter)
ἰσοσκελέστᾰτος (feminine masculine neuter superlative)

Latin: īsoscelēs

English: isosceles

Italian: isoscele

Sicilian: isòscili

ἴσος (ísos, “equal”) + σκέλος (skélos, “leg”) + -ής (-ḗs, adjective suffix)

affix

(geometry, of triangles) Having two sides equal, isosceles


σκαληνός

σκᾰληνός • (skălēnós) m (feminine σκᾰληνή, neuter σκᾰληνόν); first/second declension

σκᾰληνός (canonical)
skălēnós (romanization)
σκᾰληνή (feminine)
σκᾰληνόν (neuter)
σκᾰληνός (masculine nominative singular)
σκᾰληνή (feminine nominative singular)
σκᾰληνόν (neuter nominative singular)
σκᾰληνώ (dual masculine nominative)
σκᾰληνᾱ́ (dual feminine nominative)
σκᾰληνώ (dual neuter nominative)
σκᾰληνοί (masculine nominative plural)
σκᾰληναί (feminine nominative plural)
σκᾰληνᾰ́ (neuter nominative plural)
σκᾰληνοῦ (genitive masculine singular)
σκᾰληνῆς (feminine genitive singular)
σκᾰληνοῦ (genitive neuter singular)
σκᾰληνοῖν (dual genitive masculine)
σκᾰληναῖν (dual feminine genitive)
σκᾰληνοῖν (dual genitive neuter)
σκᾰληνῶν (genitive masculine plural)
σκᾰληνῶν (feminine genitive plural)
σκᾰληνῶν (genitive neuter plural)
σκᾰληνῷ (dative masculine singular)
σκᾰληνῇ (dative feminine singular)
σκᾰληνῷ (dative neuter singular)
σκᾰληνοῖν (dative dual masculine)
σκᾰληναῖν (dative dual feminine)
σκᾰληνοῖν (dative dual neuter)
σκᾰληνοῖς (dative masculine plural)
σκᾰληναῖς (dative feminine plural)
σκᾰληνοῖς (dative neuter plural)
σκᾰληνόν (accusative masculine singular)
σκᾰληνήν (accusative feminine singular)
σκᾰληνόν (accusative neuter singular)
σκᾰληνώ (accusative dual masculine)
σκᾰληνᾱ́ (accusative dual feminine)
σκᾰληνώ (accusative dual neuter)
σκᾰληνούς (accusative masculine plural)
σκᾰληνᾱ́ς (accusative feminine plural)
σκᾰληνᾰ́ (accusative neuter plural)
σκᾰληνέ (masculine singular vocative)
σκᾰληνή (feminine singular vocative)
σκᾰληνόν (neuter singular vocative)
σκᾰληνώ (dual masculine vocative)
σκᾰληνᾱ́ (dual feminine vocative)
σκᾰληνώ (dual neuter vocative)
σκᾰληνοί (masculine plural vocative)
σκᾰληναί (feminine plural vocative)
σκᾰληνᾰ́ (neuter plural vocative)
σκᾰληνῶς (adverbial feminine masculine neuter)
σκᾰληνότερος (comparative feminine masculine neuter)
σκᾰληνότᾰτος (feminine masculine neuter superlative)

→ Greek: σκαληνός (skalinós)

→ Latin: scalēnus

→ English: scalene, scalenus

Perhaps from Proto-Indo-European *(s)kel- (“to curve, bend”) or from *(s)kelH- (“to cut, carve, split”).

der

(geometry, of triangles) Having unequal sides, scalene.


σκαληνός

head

σκαληνός • (skalinós) m (feminine σκαληνή, neuter σκαληνό)

skalinós (romanization)
σκαληνή (feminine)
σκαληνό (neuter)
σκαληνός (masculine nominative singular)
σκαληνή (feminine nominative singular)
σκαληνό (neuter nominative singular)
σκαληνοί (masculine nominative plural)
σκαληνές (feminine nominative plural)
σκαληνά (neuter nominative plural)
σκαληνού (genitive masculine singular)
σκαληνής (feminine genitive singular)
σκαληνού (genitive neuter singular)
σκαληνών (genitive masculine plural)
σκαληνών (feminine genitive plural)
σκαληνών (genitive neuter plural)
σκαληνό (accusative masculine singular)
σκαληνή (accusative feminine singular)
σκαληνό (accusative neuter singular)
σκαληνούς (accusative masculine plural)
σκαληνές (accusative feminine plural)
σκαληνά (accusative neuter plural)
σκαληνέ (masculine singular vocative)
σκαληνή (feminine singular vocative)
σκαληνό (neuter singular vocative)
σκαληνοί (masculine plural vocative)
σκαληνές (feminine plural vocative)
σκαληνά (neuter plural vocative)

el-decl-adj-table

σκαληνός (skalinós)

σκαληνή (skaliní)

σκαληνό (skalinó)

σκαληνοί (skalinoí)

σκαληνές (skalinés)

σκαληνά (skaliná)

σκαληνού (skalinoú)

σκαληνής (skalinís)

σκαληνού (skalinoú)

σκαληνών (skalinón)

σκαληνών (skalinón)

σκαληνών (skalinón)

σκαληνό (skalinó)

σκαληνή (skaliní)

σκαληνό (skalinó)

σκαληνούς (skalinoús)

σκαληνές (skalinés)

σκαληνά (skaliná)

σκαληνέ (skaliné)

σκαληνή (skaliní)

σκαληνό (skalinó)

σκαληνοί (skalinoí)

σκαληνές (skalinés)

σκαληνά (skaliná)

(geometry) scalene, having unequal sides


trirettangolo

it-adj

trirettangolo (feminine trirettangola, masculine plural trirettangoli, feminine plural trirettangole)

trirettangola (feminine)
trirettangoli (masculine plural)
trirettangole (feminine plural)

From tri- (“three”) + rettangolo (“rectangle”).


oloid

LL-Q1860 (eng)-Flame, not lame-oloid.wav

Furthermore, we derive the expectations of the mean width, the surface area and the volume of the intersections of a fixed oloid and a moving ball, as well as of a fixed and a moving oloid.

2016, Uwe Bäsel, “The mean width of the oloid and integral geometric applications of it”, in arXiv:

(geometry) A three-dimensional curved geometric object, the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle.


aguhon

[ʔɐ.ɣʊˈhon̪]

Borrowed from Spanish agujón (“large needle”).

bor+

pair of compasses; compass for drawing circles


storsirkel

storsirkel m (definite singular storsirkelen, indefinite plural storsirkler, definite plural storsirklene)

storsirkelen (definite singular)
storsirkler (indefinite plural)
storsirklene (definite plural)


storsirkel

storsirkel m (definite singular storsirkelen, indefinite plural storsirklar, definite plural storsirklane)

storsirkelen (definite singular)
storsirklar (indefinite plural)
storsirklane (definite plural)


triangolo ottuso

it-noun

triangolo ottuso m (plural triangoli ottusi)

triangoli ottusi (plural)
triangolo ottusangolo (alternative)

From triangolo (“triangle”) + ottuso (“obtuse”).


triangolo acuto

triangolo acuto m (plural triangoli acuti)

triangoli acuti (plural)
triangolo acutangolo (alternative)

From triangolo (“triangle”) + acuto (“acute”).


triangolo ottusangolo

triangolo ottusangolo m (plural triangoli ottusangoli)

From triangolo (“triangle”) + ottusangolo (“obtuse-angled”).

triangolo ottuso
triangolo ottuso#Italian

(geometry) alternative form of triangolo ottuso


obtuza

Borrowed from English obtuse, French obtus, Italian ottuso, Spanish obtuso, from Latin obtūsus, past participle of obtundere.


triangolo acutangolo

triangolo acutangolo m (plural triangoli acutangoli)

From triangolo (“triangle”) + acutangolo (“acute-angled”).

(geometry) alternative form of triangolo acuto


spirallikeness

LL-Q1860 (eng)-Flame, not lame-spirallikeness.wav

(geometry) The property of being spirallike.


forskyde

head

forskyde (imperative forskyd, infinitive at forskyde, present tense forskyder, past tense forskød, perfect tense har forskudt)

forskyd (imperative)
at forskyde (infinitive)
forskyder (present)
forskød (past)
har forskudt (perfect)


rhombic dodecahedron

en-noun

rhombic dodecahedron (plural rhombic dodecahedra or rhombic dodecahedrons)

rhombic dodecahedra (plural)
rhombic dodecahedrons (plural)
rhombicdodecahedron (alternative)

Doing this we would find that the network which is dual to the space filling array of rhombic dodecahedra is the space filling array of tetrahedra and octahedra in which 12 edges meet at the vertices which fall at the centers of the original rhombic dodecahedra.

1990, [1978], Peter Pearce, Structure in Nature Is a Strategy for Design, page 5:

Crystallographers are familiar with the rhombic dodecahedron as a domain of reference with which to account for the growth and structure of natural crystals.

2007, Scott Eastham, American Dreamer: Bucky Fuller and the Sacred Geometry of Nature, page 160:

Rhombic Dodecahedrons appear as well in the unit cells of diamonds, four vertices absent with the chemical bonds on the remaining edges. The Rhombic Dodecahedron can be used to tessellate 3D space in a manner similar to the Cube.

2013, L. Dennis, Brender McNair, N. J. Woolf, L. H. Kauffman, “6: The Mereon 120/80 — Form Informing Function”, in Lynnclaire Dennis, Jytte Brender McNair, Louis H. Kauffman, editors, The Mereon Matrix: Unity, Perspective and Paradox, page 135:

(geometry) A convex polyhedron that has 12 congruent rhombic faces, 24 edges and 14 vertices of two types (eight 3-edge and six 4-edge) and is a Catalan solid.


Schläfli symbol

Schläfli symbol (plural Schläfli symbols)

From Schläfli (“a surname”) + symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895).

1995, Unnamed translator, E. B. Vinberg, Polynomial Group, article in M. Hazewinkel (editor), Encyclopaedia of Mathematics, Volume 4: Monge–Ampère Equation — Rings and Algebras, 2013, International Edition, page 481,
The three-dimensional regular polytopes (Platonic solids) have the following Schläfli symbols: the tetrahedron — {3, 3}, the cube — {4, 3}, the octahedron — {3, 4} — the dodecahedron — {5, 3}, and the icosahedron — {3, 5}.

For the regular tiling of squares the Schläfli symbol is {4,4}, indicating that there are four squares surrounding each vertex. And for the regular tiling of hexagons the Schläfli symbol is {6,3}, indicating that there are three hexagons surrounding each vertex.

2007, Michael E. Mortenson, chapter L, in Geometric Transformations for 3D Modeling, page 248:

The 24-cell has has 24 octahedral cells, 24 vertices, 96 triangular faces and 96 edges. Its Schläfli symbol is {3, 4, 3} from which we see that the vertex figure is a cube.

2012, John Barnes, Gems of Geometry, 2nd edition, page 79:

(geometry) A notation that recursively encodes certain properties of a specified regular polytope or tessellation.

Schläflin symboli

notation encoding certain properties of a regular polytope or tessellation


Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence.

1984, London Mathematical Society lecture note series, numbers 88-90, page 101:

The situation for 4-polytopes is fundamentally different from that for 3-dimensional polytopes. One reason is that there is no similar reduction of 4-polytope theory to a combinatorial (graph) problem.

2004, Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler, “16: Basic properties of convex polytopes”, in Joseph O'Rourke, Jacob E. Goodman, editors, Handbook of Discrete and Computational Geometry, 2nd edition, page 369:

For d = 4, Hamiltonian cycles in the regular 4-polytopes are known to exist. However, it seems that so far no decision about the existence or non-existence of 1-Hamiltonian surfaces in the 2-skeleton of any of the three sporadic regular 4-polytopes can be made, compare [120].

2011, Felix Effenberger, Hamiltonian Submanifolds of Regular Polytopes, page 40:


tetrakis hexahedron

tetrakis hexahedron (plural tetrakis hexahedra or tetrakis hexahedrons)

tetrakis hexahedra (plural)
tetrakis hexahedrons (plural)
tetrakishexahedron (alternative)
tetrakis-hexahedron (alternative)

Of the fourteen crystals examined, five were from the Karnul district (four tetrakis-hexahedra and one octahedron with tetrakis-hexahedron), one from Sambalpur (tetrakis-hexahedron with octahedron, four from Panna (much distorted tetrakis-hexahedra), the remaining four said to have come from Simla.

1904, Max Bauer, translated by L. J. Spencer, Precious Stones, volume 1, published 1968, page 154:

In the Isometric Tribe can be found the families of the Tetrakis Hexahedrons and Octahedrons, with their various descendants.

1909, Marshman Edward Wadsworth, Crystallography: An Elementary Manual for the Laboratory, page 189:

The goniometrical angle over the longer edges, that is, the angle between the normals to each pair of faces intersecting in a longer edge, in the cases of the two tetrakis hexahedra most frequently met with, has the following values:

1922, Alfred Edwin Howard Tutton, Crystallography and Practical Crystal Measurement, volume 1, page 153:

Not one exhibits plane faces or straight edges, being mostly distorted triakis-octahedra or tetrakis-hexahedra with finely striated curved faces.

1946, Mineralogical Society of America, Mineralogical Abstracts, volume 9, page 109:

Because of this another polyhedron – the tetrakis hexahedron – that has 14 vertices and 24 faces might be also a good model. The tetrakis hexahedron is slightly less regular than an icosahedron.

2010, Sumudu P. Leelananda, Yaping Feng, Pawel Gniewek, Andrzej Kloczkowski, Robert L. Jernigan, “6: Statistical Contact Potentials in Protein Coarse-Grained Modeling: From Pair to Multi-body Potentials”, in Andrzej Kolinski, editor, Multiscale Approaches to Protein Modeling, page 150:

(geometry) A Catalan solid that has 24 congruent triangular faces and 36 edges and can be imagined as a cube with a square pyramid on each face.

tetrakis-heksaedri

polyhedron with 24 triangular faces and 36 edges


Schlegel diagram

Schlegel diagram (plural Schlegel diagrams)

From Schlegel (“a surname”) + diagram, after German mathematician Victor Schlegel, who introduced the diagram in 1886.

The location of the point x₀ can always be chosen so that the edges in the Schlegel diagram can be drawn as non-intersecting straight lines.

1999, R. B. King, “1: Topology in Chemistry”, in D Bonchev, D.H Rouvray, editors, Chemical Topology: Introduction and Fundamentals, page 21:

Schlegel diagrams are a useful way to explore how these polyhedra can be linked (Hoppe and Köhler 1988).

2002, Ian David Brown, chapter L, in The Chemical Bond in Inorganic Chemistry: The Bond Valence, page 150:

These structures may all be represented on a planar surface by their Schlegel diagrams. A polyhedron Schlegel diagram is its networks of edges and vertices drawn in a special way: if you hold the polyhedron so close to your face that one of faces frames the entire polyhedron and you see all the other edges meeting inside that frame, then you have a Schlegel diagram.

2013, Arthur L. Loeb, “5: Polyhedra: Surfaces or Solids?”, in Marjorie Senechal, editor, Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination, page 69:

(geometry) A projection of a polytope from n-dimensional space to n-1 dimensions through a point beyond one of its faces; especially such a projection (itself represented in 2 dimensions) of a 3- or 4-dimensional polytope.


餘角

/y³⁵ t͡ɕi̯ɑʊ̯²¹⁴⁻²¹⁽⁴⁾/

/y³⁵ t͡ɕi̯aʊ̯ɻʷ²¹⁴⁻²¹⁽⁴⁾/

/jyː²¹ kɔːk̚³/

/y³⁵ t͡ɕi̯ɑʊ̯²¹⁴⁻²¹⁽⁴⁾/

/y³⁵ t͡ɕi̯aʊ̯ɻʷ²¹⁴⁻²¹⁽⁴⁾/

/jyː²¹ kɔːk̚³/


projektiopinta

projektiopinta (nominative singular)
projektiopinnat (nominative plural)
projektiopinta (accusative nominative singular)
projektiopinnat (accusative nominative plural)
projektiopinnan (accusative genitive singular)
projektiopinnat (accusative genitive plural)
projektiopinnan (genitive singular)
projektiopintojen (genitive plural)
projektiopintain (genitive plural rare)
projektiopintaa (partitive singular)
projektiopintoja (partitive plural)
projektiopinnassa (inessive singular)
projektiopinnoissa (inessive plural)
projektiopinnasta (elative singular)
projektiopinnoista (elative plural)
projektiopintaan (illative singular)
projektiopintoihin (illative plural)
projektiopinnalla (adessive singular)
projektiopinnoilla (adessive plural)
projektiopinnalta (ablative singular)
projektiopinnoilta (ablative plural)
projektiopinnalle (allative singular)
projektiopinnoille (allative plural)
projektiopintana (essive singular)
projektiopintoina (essive plural)
projektiopinnaksi (singular translative)
projektiopinnoiksi (plural translative)
projektiopinnatta (abessive singular)
projektiopinnoitta (abessive plural)
projektiopinnoin (instructive plural)
See the possessive forms below. (comitative)
projektiopintani (nominative singular)
projektiopintani (nominative plural)
projektiopintani (accusative nominative singular)
projektiopintani (accusative nominative plural)
projektiopintani (accusative genitive singular)
projektiopintani (accusative genitive plural)
projektiopintani (genitive singular)
projektiopintojeni (genitive plural)
projektiopintaini (genitive plural rare)
projektiopintaani (partitive singular)
projektiopintojani (partitive plural)
projektiopinnassani (inessive singular)
projektiopinnoissani (inessive plural)
projektiopinnastani (elative singular)
projektiopinnoistani (elative plural)
projektiopintaani (illative singular)
projektiopintoihini (illative plural)
projektiopinnallani (adessive singular)
projektiopinnoillani (adessive plural)
projektiopinnaltani (ablative singular)
projektiopinnoiltani (ablative plural)
projektiopinnalleni (allative singular)
projektiopinnoilleni (allative plural)
projektiopintanani (essive singular)
projektiopintoinani (essive plural)
projektiopinnakseni (singular translative)
projektiopinnoikseni (plural translative)
projektiopinnattani (abessive singular)
projektiopinnoittani (abessive plural)
projektiopintoineni (comitative plural)
projektiopintasi (nominative singular)
projektiopintasi (nominative plural)
projektiopintasi (accusative nominative singular)
projektiopintasi (accusative nominative plural)
projektiopintasi (accusative genitive singular)
projektiopintasi (accusative genitive plural)
projektiopintasi (genitive singular)
projektiopintojesi (genitive plural)
projektiopintaisi (genitive plural rare)
projektiopintaasi (partitive singular)
projektiopintojasi (partitive plural)
projektiopinnassasi (inessive singular)
projektiopinnoissasi (inessive plural)
projektiopinnastasi (elative singular)
projektiopinnoistasi (elative plural)
projektiopintaasi (illative singular)
projektiopintoihisi (illative plural)
projektiopinnallasi (adessive singular)
projektiopinnoillasi (adessive plural)
projektiopinnaltasi (ablative singular)
projektiopinnoiltasi (ablative plural)
projektiopinnallesi (allative singular)
projektiopinnoillesi (allative plural)
projektiopintanasi (essive singular)
projektiopintoinasi (essive plural)
projektiopinnaksesi (singular translative)
projektiopinnoiksesi (plural translative)
projektiopinnattasi (abessive singular)
projektiopinnoittasi (abessive plural)
projektiopintoinesi (comitative plural)
projektiopintamme (nominative singular)
projektiopintamme (nominative plural)
projektiopintamme (accusative nominative singular)
projektiopintamme (accusative nominative plural)
projektiopintamme (accusative genitive singular)
projektiopintamme (accusative genitive plural)
projektiopintamme (genitive singular)
projektiopintojemme (genitive plural)
projektiopintaimme (genitive plural rare)
projektiopintaamme (partitive singular)
projektiopintojamme (partitive plural)
projektiopinnassamme (inessive singular)
projektiopinnoissamme (inessive plural)
projektiopinnastamme (elative singular)
projektiopinnoistamme (elative plural)
projektiopintaamme (illative singular)
projektiopintoihimme (illative plural)
projektiopinnallamme (adessive singular)
projektiopinnoillamme (adessive plural)
projektiopinnaltamme (ablative singular)
projektiopinnoiltamme (ablative plural)
projektiopinnallemme (allative singular)
projektiopinnoillemme (allative plural)
projektiopintanamme (essive singular)
projektiopintoinamme (essive plural)
projektiopinnaksemme (singular translative)
projektiopinnoiksemme (plural translative)
projektiopinnattamme (abessive singular)
projektiopinnoittamme (abessive plural)
projektiopintoinemme (comitative plural)
projektiopintanne (nominative singular)
projektiopintanne (nominative plural)
projektiopintanne (accusative nominative singular)
projektiopintanne (accusative nominative plural)
projektiopintanne (accusative genitive singular)
projektiopintanne (accusative genitive plural)
projektiopintanne (genitive singular)
projektiopintojenne (genitive plural)
projektiopintainne (genitive plural rare)
projektiopintaanne (partitive singular)
projektiopintojanne (partitive plural)
projektiopinnassanne (inessive singular)
projektiopinnoissanne (inessive plural)
projektiopinnastanne (elative singular)
projektiopinnoistanne (elative plural)
projektiopintaanne (illative singular)
projektiopintoihinne (illative plural)
projektiopinnallanne (adessive singular)
projektiopinnoillanne (adessive plural)
projektiopinnaltanne (ablative singular)
projektiopinnoiltanne (ablative plural)
projektiopinnallenne (allative singular)
projektiopinnoillenne (allative plural)
projektiopintananne (essive singular)
projektiopintoinanne (essive plural)
projektiopinnaksenne (singular translative)
projektiopinnoiksenne (plural translative)
projektiopinnattanne (abessive singular)
projektiopinnoittanne (abessive plural)
projektiopintoinenne (comitative plural)
projektiopintansa (nominative singular)
projektiopintansa (nominative plural)
projektiopintansa (accusative nominative singular)
projektiopintansa (accusative nominative plural)
projektiopintansa (accusative genitive singular)
projektiopintansa (accusative genitive plural)
projektiopintansa (genitive singular)
projektiopintojensa (genitive plural)
projektiopintainsa (genitive plural rare)
projektiopintaansa (partitive singular)
projektiopintojaan (partitive plural)
projektiopintojansa (partitive plural)
projektiopinnassaan (inessive singular)
projektiopinnassansa (inessive singular)
projektiopinnoissaan (inessive plural)
projektiopinnoissansa (inessive plural)
projektiopinnastaan (elative singular)
projektiopinnastansa (elative singular)
projektiopinnoistaan (elative plural)
projektiopinnoistansa (elative plural)
projektiopintaansa (illative singular)
projektiopintoihinsa (illative plural)
projektiopinnallaan (adessive singular)
projektiopinnallansa (adessive singular)
projektiopinnoillaan (adessive plural)
projektiopinnoillansa (adessive plural)
projektiopinnaltaan (ablative singular)
projektiopinnaltansa (ablative singular)
projektiopinnoiltaan (ablative plural)
projektiopinnoiltansa (ablative plural)
projektiopinnalleen (allative singular)
projektiopinnallensa (allative singular)
projektiopinnoilleen (allative plural)
projektiopinnoillensa (allative plural)
projektiopintanaan (essive singular)
projektiopintanansa (essive singular)
projektiopintoinaan (essive plural)
projektiopintoinansa (essive plural)
projektiopinnakseen (singular translative)
projektiopinnaksensa (singular translative)
projektiopinnoikseen (plural translative)
projektiopinnoiksensa (plural translative)
projektiopinnattaan (abessive singular)
projektiopinnattansa (abessive singular)
projektiopinnoittaan (abessive plural)
projektiopinnoittansa (abessive plural)
projektiopintoineen (comitative plural)
projektiopintoinensa (comitative plural)

projektio (“projection”) + pinta (“surface”)

compound

(geometry) viewing surface (in orthographic projection, the surface onto which an object is projected)


projektiotaso

projektiotaso (nominative singular)
projektiotasot (nominative plural)
projektiotaso (accusative nominative singular)
projektiotasot (accusative nominative plural)
projektiotason (accusative genitive singular)
projektiotasot (accusative genitive plural)
projektiotason (genitive singular)
projektiotasojen (genitive plural)
projektiotasoa (partitive singular)
projektiotasoja (partitive plural)
projektiotasossa (inessive singular)
projektiotasoissa (inessive plural)
projektiotasosta (elative singular)
projektiotasoista (elative plural)
projektiotasoon (illative singular)
projektiotasoihin (illative plural)
projektiotasolla (adessive singular)
projektiotasoilla (adessive plural)
projektiotasolta (ablative singular)
projektiotasoilta (ablative plural)
projektiotasolle (allative singular)
projektiotasoille (allative plural)
projektiotasona (essive singular)
projektiotasoina (essive plural)
projektiotasoksi (singular translative)
projektiotasoiksi (plural translative)
projektiotasotta (abessive singular)
projektiotasoitta (abessive plural)
projektiotasoin (instructive plural)
See the possessive forms below. (comitative)
projektiotasoni (nominative singular)
projektiotasoni (nominative plural)
projektiotasoni (accusative nominative singular)
projektiotasoni (accusative nominative plural)
projektiotasoni (accusative genitive singular)
projektiotasoni (accusative genitive plural)
projektiotasoni (genitive singular)
projektiotasojeni (genitive plural)
projektiotasoani (partitive singular)
projektiotasojani (partitive plural)
projektiotasossani (inessive singular)
projektiotasoissani (inessive plural)
projektiotasostani (elative singular)
projektiotasoistani (elative plural)
projektiotasooni (illative singular)
projektiotasoihini (illative plural)
projektiotasollani (adessive singular)
projektiotasoillani (adessive plural)
projektiotasoltani (ablative singular)
projektiotasoiltani (ablative plural)
projektiotasolleni (allative singular)
projektiotasoilleni (allative plural)
projektiotasonani (essive singular)
projektiotasoinani (essive plural)
projektiotasokseni (singular translative)
projektiotasoikseni (plural translative)
projektiotasottani (abessive singular)
projektiotasoittani (abessive plural)
projektiotasoineni (comitative plural)
projektiotasosi (nominative singular)
projektiotasosi (nominative plural)
projektiotasosi (accusative nominative singular)
projektiotasosi (accusative nominative plural)
projektiotasosi (accusative genitive singular)
projektiotasosi (accusative genitive plural)
projektiotasosi (genitive singular)
projektiotasojesi (genitive plural)
projektiotasoasi (partitive singular)
projektiotasojasi (partitive plural)
projektiotasossasi (inessive singular)
projektiotasoissasi (inessive plural)
projektiotasostasi (elative singular)
projektiotasoistasi (elative plural)
projektiotasoosi (illative singular)
projektiotasoihisi (illative plural)
projektiotasollasi (adessive singular)
projektiotasoillasi (adessive plural)
projektiotasoltasi (ablative singular)
projektiotasoiltasi (ablative plural)
projektiotasollesi (allative singular)
projektiotasoillesi (allative plural)
projektiotasonasi (essive singular)
projektiotasoinasi (essive plural)
projektiotasoksesi (singular translative)
projektiotasoiksesi (plural translative)
projektiotasottasi (abessive singular)
projektiotasoittasi (abessive plural)
projektiotasoinesi (comitative plural)
projektiotasomme (nominative singular)
projektiotasomme (nominative plural)
projektiotasomme (accusative nominative singular)
projektiotasomme (accusative nominative plural)
projektiotasomme (accusative genitive singular)
projektiotasomme (accusative genitive plural)
projektiotasomme (genitive singular)
projektiotasojemme (genitive plural)
projektiotasoamme (partitive singular)
projektiotasojamme (partitive plural)
projektiotasossamme (inessive singular)
projektiotasoissamme (inessive plural)
projektiotasostamme (elative singular)
projektiotasoistamme (elative plural)
projektiotasoomme (illative singular)
projektiotasoihimme (illative plural)
projektiotasollamme (adessive singular)
projektiotasoillamme (adessive plural)
projektiotasoltamme (ablative singular)
projektiotasoiltamme (ablative plural)
projektiotasollemme (allative singular)
projektiotasoillemme (allative plural)
projektiotasonamme (essive singular)
projektiotasoinamme (essive plural)
projektiotasoksemme (singular translative)
projektiotasoiksemme (plural translative)
projektiotasottamme (abessive singular)
projektiotasoittamme (abessive plural)
projektiotasoinemme (comitative plural)
projektiotasonne (nominative singular)
projektiotasonne (nominative plural)
projektiotasonne (accusative nominative singular)
projektiotasonne (accusative nominative plural)
projektiotasonne (accusative genitive singular)
projektiotasonne (accusative genitive plural)
projektiotasonne (genitive singular)
projektiotasojenne (genitive plural)
projektiotasoanne (partitive singular)
projektiotasojanne (partitive plural)
projektiotasossanne (inessive singular)
projektiotasoissanne (inessive plural)
projektiotasostanne (elative singular)
projektiotasoistanne (elative plural)
projektiotasoonne (illative singular)
projektiotasoihinne (illative plural)
projektiotasollanne (adessive singular)
projektiotasoillanne (adessive plural)
projektiotasoltanne (ablative singular)
projektiotasoiltanne (ablative plural)
projektiotasollenne (allative singular)
projektiotasoillenne (allative plural)
projektiotasonanne (essive singular)
projektiotasoinanne (essive plural)
projektiotasoksenne (singular translative)
projektiotasoiksenne (plural translative)
projektiotasottanne (abessive singular)
projektiotasoittanne (abessive plural)
projektiotasoinenne (comitative plural)
projektiotasonsa (nominative singular)
projektiotasonsa (nominative plural)
projektiotasonsa (accusative nominative singular)
projektiotasonsa (accusative nominative plural)
projektiotasonsa (accusative genitive singular)
projektiotasonsa (accusative genitive plural)
projektiotasonsa (genitive singular)
projektiotasojensa (genitive plural)
projektiotasoaan (partitive singular)
projektiotasoansa (partitive singular)
projektiotasojaan (partitive plural)
projektiotasojansa (partitive plural)
projektiotasossaan (inessive singular)
projektiotasossansa (inessive singular)
projektiotasoissaan (inessive plural)
projektiotasoissansa (inessive plural)
projektiotasostaan (elative singular)
projektiotasostansa (elative singular)
projektiotasoistaan (elative plural)
projektiotasoistansa (elative plural)
projektiotasoonsa (illative singular)
projektiotasoihinsa (illative plural)
projektiotasollaan (adessive singular)
projektiotasollansa (adessive singular)
projektiotasoillaan (adessive plural)
projektiotasoillansa (adessive plural)
projektiotasoltaan (ablative singular)
projektiotasoltansa (ablative singular)
projektiotasoiltaan (ablative plural)
projektiotasoiltansa (ablative plural)
projektiotasolleen (allative singular)
projektiotasollensa (allative singular)
projektiotasoilleen (allative plural)
projektiotasoillensa (allative plural)
projektiotasonaan (essive singular)
projektiotasonansa (essive singular)
projektiotasoinaan (essive plural)
projektiotasoinansa (essive plural)
projektiotasokseen (singular translative)
projektiotasoksensa (singular translative)
projektiotasoikseen (plural translative)
projektiotasoiksensa (plural translative)
projektiotasottaan (abessive singular)
projektiotasottansa (abessive singular)
projektiotasoittaan (abessive plural)
projektiotasoittansa (abessive plural)
projektiotasoineen (comitative plural)
projektiotasoinensa (comitative plural)

projektio (“projection”) + taso (“plane”)


projektiokuva

projektiokuva (nominative singular)
projektiokuvat (nominative plural)
projektiokuva (accusative nominative singular)
projektiokuvat (accusative nominative plural)
projektiokuvan (accusative genitive singular)
projektiokuvat (accusative genitive plural)
projektiokuvan (genitive singular)
projektiokuvien (genitive plural)
projektiokuvain (genitive plural rare)
projektiokuvaa (partitive singular)
projektiokuvia (partitive plural)
projektiokuvassa (inessive singular)
projektiokuvissa (inessive plural)
projektiokuvasta (elative singular)
projektiokuvista (elative plural)
projektiokuvaan (illative singular)
projektiokuviin (illative plural)
projektiokuvalla (adessive singular)
projektiokuvilla (adessive plural)
projektiokuvalta (ablative singular)
projektiokuvilta (ablative plural)
projektiokuvalle (allative singular)
projektiokuville (allative plural)
projektiokuvana (essive singular)
projektiokuvina (essive plural)
projektiokuvaksi (singular translative)
projektiokuviksi (plural translative)
projektiokuvatta (abessive singular)
projektiokuvitta (abessive plural)
projektiokuvin (instructive plural)
See the possessive forms below. (comitative)
projektiokuvani (nominative singular)
projektiokuvani (nominative plural)
projektiokuvani (accusative nominative singular)
projektiokuvani (accusative nominative plural)
projektiokuvani (accusative genitive singular)
projektiokuvani (accusative genitive plural)
projektiokuvani (genitive singular)
projektiokuvieni (genitive plural)
projektiokuvaini (genitive plural rare)
projektiokuvaani (partitive singular)
projektiokuviani (partitive plural)
projektiokuvassani (inessive singular)
projektiokuvissani (inessive plural)
projektiokuvastani (elative singular)
projektiokuvistani (elative plural)
projektiokuvaani (illative singular)
projektiokuviini (illative plural)
projektiokuvallani (adessive singular)
projektiokuvillani (adessive plural)
projektiokuvaltani (ablative singular)
projektiokuviltani (ablative plural)
projektiokuvalleni (allative singular)
projektiokuvilleni (allative plural)
projektiokuvanani (essive singular)
projektiokuvinani (essive plural)
projektiokuvakseni (singular translative)
projektiokuvikseni (plural translative)
projektiokuvattani (abessive singular)
projektiokuvittani (abessive plural)
projektiokuvineni (comitative plural)
projektiokuvasi (nominative singular)
projektiokuvasi (nominative plural)
projektiokuvasi (accusative nominative singular)
projektiokuvasi (accusative nominative plural)
projektiokuvasi (accusative genitive singular)
projektiokuvasi (accusative genitive plural)
projektiokuvasi (genitive singular)
projektiokuviesi (genitive plural)
projektiokuvaisi (genitive plural rare)
projektiokuvaasi (partitive singular)
projektiokuviasi (partitive plural)
projektiokuvassasi (inessive singular)
projektiokuvissasi (inessive plural)
projektiokuvastasi (elative singular)
projektiokuvistasi (elative plural)
projektiokuvaasi (illative singular)
projektiokuviisi (illative plural)
projektiokuvallasi (adessive singular)
projektiokuvillasi (adessive plural)
projektiokuvaltasi (ablative singular)
projektiokuviltasi (ablative plural)
projektiokuvallesi (allative singular)
projektiokuvillesi (allative plural)
projektiokuvanasi (essive singular)
projektiokuvinasi (essive plural)
projektiokuvaksesi (singular translative)
projektiokuviksesi (plural translative)
projektiokuvattasi (abessive singular)
projektiokuvittasi (abessive plural)
projektiokuvinesi (comitative plural)
projektiokuvamme (nominative singular)
projektiokuvamme (nominative plural)
projektiokuvamme (accusative nominative singular)
projektiokuvamme (accusative nominative plural)
projektiokuvamme (accusative genitive singular)
projektiokuvamme (accusative genitive plural)
projektiokuvamme (genitive singular)
projektiokuviemme (genitive plural)
projektiokuvaimme (genitive plural rare)
projektiokuvaamme (partitive singular)
projektiokuviamme (partitive plural)
projektiokuvassamme (inessive singular)
projektiokuvissamme (inessive plural)
projektiokuvastamme (elative singular)
projektiokuvistamme (elative plural)
projektiokuvaamme (illative singular)
projektiokuviimme (illative plural)
projektiokuvallamme (adessive singular)
projektiokuvillamme (adessive plural)
projektiokuvaltamme (ablative singular)
projektiokuviltamme (ablative plural)
projektiokuvallemme (allative singular)
projektiokuvillemme (allative plural)
projektiokuvanamme (essive singular)
projektiokuvinamme (essive plural)
projektiokuvaksemme (singular translative)
projektiokuviksemme (plural translative)
projektiokuvattamme (abessive singular)
projektiokuvittamme (abessive plural)
projektiokuvinemme (comitative plural)
projektiokuvanne (nominative singular)
projektiokuvanne (nominative plural)
projektiokuvanne (accusative nominative singular)
projektiokuvanne (accusative nominative plural)
projektiokuvanne (accusative genitive singular)
projektiokuvanne (accusative genitive plural)
projektiokuvanne (genitive singular)
projektiokuvienne (genitive plural)
projektiokuvainne (genitive plural rare)
projektiokuvaanne (partitive singular)
projektiokuvianne (partitive plural)
projektiokuvassanne (inessive singular)
projektiokuvissanne (inessive plural)
projektiokuvastanne (elative singular)
projektiokuvistanne (elative plural)
projektiokuvaanne (illative singular)
projektiokuviinne (illative plural)
projektiokuvallanne (adessive singular)
projektiokuvillanne (adessive plural)
projektiokuvaltanne (ablative singular)
projektiokuviltanne (ablative plural)
projektiokuvallenne (allative singular)
projektiokuvillenne (allative plural)
projektiokuvananne (essive singular)
projektiokuvinanne (essive plural)
projektiokuvaksenne (singular translative)
projektiokuviksenne (plural translative)
projektiokuvattanne (abessive singular)
projektiokuvittanne (abessive plural)
projektiokuvinenne (comitative plural)
projektiokuvansa (nominative singular)
projektiokuvansa (nominative plural)
projektiokuvansa (accusative nominative singular)
projektiokuvansa (accusative nominative plural)
projektiokuvansa (accusative genitive singular)
projektiokuvansa (accusative genitive plural)
projektiokuvansa (genitive singular)
projektiokuviensa (genitive plural)
projektiokuvainsa (genitive plural rare)
projektiokuvaansa (partitive singular)
projektiokuviaan (partitive plural)
projektiokuviansa (partitive plural)
projektiokuvassaan (inessive singular)
projektiokuvassansa (inessive singular)
projektiokuvissaan (inessive plural)
projektiokuvissansa (inessive plural)
projektiokuvastaan (elative singular)
projektiokuvastansa (elative singular)
projektiokuvistaan (elative plural)
projektiokuvistansa (elative plural)
projektiokuvaansa (illative singular)
projektiokuviinsa (illative plural)
projektiokuvallaan (adessive singular)
projektiokuvallansa (adessive singular)
projektiokuvillaan (adessive plural)
projektiokuvillansa (adessive plural)
projektiokuvaltaan (ablative singular)
projektiokuvaltansa (ablative singular)
projektiokuviltaan (ablative plural)
projektiokuviltansa (ablative plural)
projektiokuvalleen (allative singular)
projektiokuvallensa (allative singular)
projektiokuvilleen (allative plural)
projektiokuvillensa (allative plural)
projektiokuvanaan (essive singular)
projektiokuvanansa (essive singular)
projektiokuvinaan (essive plural)
projektiokuvinansa (essive plural)
projektiokuvakseen (singular translative)
projektiokuvaksensa (singular translative)
projektiokuvikseen (plural translative)
projektiokuviksensa (plural translative)
projektiokuvattaan (abessive singular)
projektiokuvattansa (abessive singular)
projektiokuvittaan (abessive plural)
projektiokuvittansa (abessive plural)
projektiokuvineen (comitative plural)
projektiokuvinensa (comitative plural)

projektio (“projection”) + kuva (“image”)

(geometry) projection (image of an object on a surface of fewer dimensions)


zuzen

zuzen (absolutive indefinite)
zuzena (absolutive indefinite singular)
zuzenak (absolutive indefinite plural)
zuzenek (ergative indefinite)
zuzenak (ergative indefinite singular)
zuzenek (ergative indefinite plural)
zuzeni (dative indefinite)
zuzenari (dative indefinite singular)
zuzenei (dative indefinite plural)
zuzenen (genitive indefinite)
zuzenaren (genitive indefinite singular)
zuzenen (genitive indefinite plural)
zuzenekin (comitative indefinite)
zuzenarekin (comitative indefinite singular)
zuzenekin (comitative indefinite plural)
zuzenengatik (causative indefinite)
zuzenarengatik (causative indefinite singular)
zuzenengatik (causative indefinite plural)
zuzenentzat (benefactive indefinite)
zuzenarentzat (benefactive indefinite singular)
zuzenentzat (benefactive indefinite plural)
zuzenez (indefinite instrumental)
zuzenaz (indefinite instrumental singular)
zuzenez (indefinite instrumental plural)
zuzenetan (indefinite inessive)
zuzenean (indefinite inessive singular)
zuzenetan (indefinite inessive plural)
zuzenetako (indefinite locative)
zuzeneko (indefinite locative singular)
zuzenetako (indefinite locative plural)
zuzenetara (allative indefinite)
zuzenera (allative indefinite singular)
zuzenetara (allative indefinite plural)
zuzenetaraino (indefinite terminative)
zuzeneraino (indefinite singular terminative)
zuzenetaraino (indefinite plural terminative)
zuzenetarantz (directive indefinite)
zuzenerantz (directive indefinite singular)
zuzenetarantz (directive indefinite plural)
zuzenetarako (destinative indefinite)
zuzenerako (destinative indefinite singular)
zuzenetarako (destinative indefinite plural)
zuzenetatik (ablative indefinite)
zuzenetik (ablative indefinite singular)
zuzenetatik (ablative indefinite plural)
zuzenik (indefinite partitive)
zuzentzat (indefinite prolative)


angular defect

Prop. XVI. If the angular defects of two triangles are equal, the areas of the triangles are equal.

1864, Transactions of the Royal Society of Edinburgh, volume 23, page 444:

We have seen that under any reasonable definition of area, the angular defect of a triangle is proportional to its area.

1995, Arlan Ramsay, Robert D. Richtmyer, Introduction to Hyperbolic Geometry, page 120:

In hyperbolic geometry, similar triangles do not exist and the area of a triangle is directly proportional to its angular defect[…].

1998, Kappa Mu Epsilon, The Pentagon: A Mathematics Magazine for Students, page 7:

(geometry, non-Euclidean geometry) The amount by which the sum of the interior angles of a triangle is less than 180° (π radians); the amount by which the sum of the internal angles of a polygon is less than what would be expected on the Euclidean plane.

angular deficiency

amount by which the total of the interior angles of a polygon is less than on the Euclidean plane

The angular defect clearly has something to do with curvature, because the larger it is, the more pointed the surface is at the vertex.

2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, page 604:

2014, C. R. Calladine, The Static-geometric Analogy in the Equations of Thin Shell Structures, W. Olszak, Thin Shell Theory: New Trends and Applications, page 294,
Figure 4(c) shows a flattened view of a small part of the undeformed polygonalized S-surface, consisting of the triangles surrounding a particular vertex. When the S-surface is strained there will be a consequent change of angular defect, which we wish to calculate.

2015, Jan Guichelaar (translator and editor), Alex Van Den Brandhof, Arnout Jaspers (editors), Half a Century of Pythagoras Magazine, page 164,
Theorem. For a spherical polyhedron the total angular defect equals 720°.

(geometry) The amount by which the total of the angles around a vertex of a polyhedron is less than 360° (2π radians).


កាំ

From Proto-Austroasiatic *kam (“arrow”).


symmetry group

[The] situation is more delicate in the case of higher dimensional symmetry groups; it is not in general possible to reduce the order of an equation invariant under an r-parameter symmetry group by r using only quadratures.

1993, Peter J. Olver, Applications of Lie Groups to Differential Equations, published 2000, page 76:

It is often assumed that the design unit inside each fundamental region (particularly for monotranslational symmetry groups p111 and p1a1 and ditranslational symmetry groups p1 and pg) is asymmetric.

2000, C. E. Horne, Geometric Symmetry in Patterns and Tilings, page 79:

The structure of the symmetry group of a molecule affects several spectroscopic aspects and vice versa. Thus, it is clearly important to know the possible symmetries of fullerenes and similar structures.
In this chapter, we study symmetry groups of fulleroids.

2010, Stanislav Jendrol, František Kardoš, “28: Symmetry of Fulleroids”, in Klaus D. Sattler, editor, Handbook of Nanophysics: Clusters and Fullerenes, pages 28–1:

(geometry, algebra, group theory) A group whose elements are all the transformations under which a given object remains invariant and whose group operation is function composition.

full symmetry group

emphasises the inclusion of orientation-reversing transformations


vinkelhalveringslinie

head

vinkelhalveringslinie c (singular definite vinkelhalveringslinien, plural indefinite vinkelhalveringslinier)

vinkelhalveringslinien (definite singular)
vinkelhalveringslinier (indefinite plural)
vinkelhalveringslinie (indefinite nominative singular)
vinkelhalveringslinien (definite nominative singular)
vinkelhalveringslinier (indefinite nominative plural)
vinkelhalveringslinierne (definite nominative plural)
vinkelhalveringslinies (genitive indefinite singular)
vinkelhalveringsliniens (definite genitive singular)
vinkelhalveringsliniers (genitive indefinite plural)
vinkelhalveringsliniernes (definite genitive plural)
vinkelhalveringslinje (alternative)

vinkel (“angle”) + halvering (“halfing”) + linie (“line”)


vinkelhalveringslinje

head

vinkelhalveringslinje c (singular definite vinkelhalveringslinjen, plural indefinite vinkelhalveringslinjer)

vinkelhalveringslinjen (definite singular)
vinkelhalveringslinjer (indefinite plural)
vinkelhalveringslinje (indefinite nominative singular)
vinkelhalveringslinjen (definite nominative singular)
vinkelhalveringslinjer (indefinite nominative plural)
vinkelhalveringslinjerne (definite nominative plural)
vinkelhalveringslinjes (genitive indefinite singular)
vinkelhalveringslinjens (definite genitive singular)
vinkelhalveringslinjers (genitive indefinite plural)
vinkelhalveringslinjernes (definite genitive plural)

(geometry) alternative spelling of vinkelhalveringslinie


midtnormal

midtnormal c (singular definite midtnormalen, plural indefinite midtnormaler)

midtnormalen (definite singular)
midtnormaler (indefinite plural)
midtnormal (indefinite nominative singular)
midtnormalen (definite nominative singular)
midtnormaler (indefinite nominative plural)
midtnormalerne (definite nominative plural)
midtnormals (genitive indefinite singular)
midtnormalens (definite genitive singular)
midtnormalers (genitive indefinite plural)
midtnormalernes (definite genitive plural)

(geometry) A line perpendicular to a segment which it intersects at that segment's midpoint; the perpendicular bisector of a segment.


εξάγωνο

exágono (romanization)
εξάγωνα (plural)
εξάγωνο (nominative singular)
εξάγωνα (nominative plural)
εξαγώνου (genitive singular)
εξάγωνου (genitive singular)
εξαγώνων (genitive plural)
εξάγωνο (accusative singular)
εξάγωνα (accusative plural)
εξάγωνο (singular vocative)
εξάγωνα (plural vocative)


cross-polytope

cross-polytopes (plural)
cross polytope (alternative)

The case p = 1, which is actually important to us, is illustrated in Figure 1.14; we are looking at the intersection of a cross-polytope with the probability simplex.

2006, Ingemar Bengtsson, Karol Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, page 25:

2008, Robert Erdahl, Andrei Ordine, Konstantin Rybnikov, Perfect Delaunay Polytopes and Perfect Quadratic Functions on Lattices, Matthias Beck, et al. (editors), Contemporary Mathematics 452: Integer Points in Polyhedra — Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics, AMS-IMS-SIAM Joint Summer Conference, June 11-15, 2006, page 104,
The convex hulls of such crosses often appear as cells in Delaunay tilings – cross polytopes are examples, as are the more spectacular symmetric perfect Delaunay polytopes.

The cross polytope βₙ is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (±1,0,0,...,0), and has therefore 2n vertices. It is named so because its vertices are located equidistant from the origin, along the Cartesian axes in n-space. The cross polytope in n dimensions is bounded by 2ⁿ (n - 1)-simplices, has 2n vertices and 2ⁿ(n - 1) edges.

2009, Herbert W. Hamber, Quantum Gravitation: The Feynman Path Integral Approach, Springer, page 263:

If one works with the l₁ norm, a ball (the set of all points whose distance lies within a certain radius around a point of interest) has the shape of a cross-polytope. A one-dimensional cross-polytope is a line segment, a two-dimensional cross-polytope is a square, for three dimensions, an octahedron, and so forth.

2010, Rainer Typke, Agatha Walczak-Typke, “Indexing Techniques for Non-metric Music Dissimilarity Measures”, in Zbigniew W. Raś, Alicja A. Wieczorkowska, editors, Advances in Music Information Retrieval, Springer, page 10:

While centrally symmetric d-polytopes with 2d vertices are affinely equivalent to the d-dimensional cross-polytope, a complete classification of the centrally symmetric d-polytopes with 2d + 2 vertices is out of reach.

2003, Branko Grünbaum, Convex Polytopes, 2nd edition, Springer, page 121b:

(geometry) A polytope that is the convex hull of points, two on each Cartesian axis of a Euclidean space, that are equidistant from the origin; an orthoplex.


Coxeter diagram

en-noun

Coxeter diagram (plural Coxeter diagrams)

It suffices to make use of the tables above and observe that the Coxeter diagram of a direct sum of C-matrices is the disconnected union of the Coxeter diagrams of the summands.
For the description of C⁻-matrices satisfying condition (2) we shall use Coxeter diagrams with the additional stipulation that in case aᵢⱼ < −1 the vertices vᵢ and vⱼ are joined by a dotted line with index −aᵢⱼ. By the Coxeter diagram of a Coxeter polyhedron and a lattice generated by reflections we mean the Coxeter diagram of the corresponding C⁻-matrix.

1991, Gregori A. Margulis, Discrete Subgroups of Semisimple Lie Groups, page 358:

An automorphism of a Coxeter diagram M leads in a natural way to a Coxeter subgroup of the Coxeter group of type M. We introduce admissible partitions of Coxeter diagrams in order to generalize this situation.

1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. Buekenhout, J. Doyen, F. de Clerck, J. A. Thas, J. W. P. Hirschfeld, editors, Finite Geometries and Combinatorics, 2nd International Conference, page 277:

The Coxeter diagrams of type E₇ and E₈ have no nontrivial automorphisms, so σ₀ is trivial in those cases.[…]The Coxeter diagram of type F₄ has a unique nontrivial automorphism, but σ₀ is trivial in this case. One can see this by using the Dynkin diagram instead of the Coxeter diagram and noting that it does not have any nontrivial automorphisms.

2008, Peter Abramenko, Kenneth S. Brown, Buildings: Theory and Applications, page 259:

Coxeter-Dynkin diagram
Coxeter-Dynkin diagram

(geometry, algebra) A Coxeter-Dynkin diagram.


hyperellipsoidal

LL-Q1860 (eng)-Flame, not lame-hyperellipsoidal.wav

A regularized Mahalanobis distance can be used for extracting hyperellipsoidal clusters [30 ].

2015 December 12, “A Comparison Study on Similarity and Dissimilarity Measures in Clustering Continuous Data”, in PLOS ONE, →DOI:

(geometry) Relating to, or having the form of a hyperellipsoid


hyperellipsoid

LL-Q1860 (eng)-Flame, not lame-hyperellipsoid.wav

(geometry) A figure, related to the hypersphere, having ellipsoidal rather than spherical symmetry


théorème de Pythagore

LL-Q150 (fra)-WikiLucas00-théorème de Pythagore.wav

(geometry, functional analysis) the Pythagorean theorem


equitangential

LL-Q1860 (eng)-Flame, not lame-equitangential.wav

(geometry) Of a curve: having tangential segments that are all of the same length.


triacontagon

LL-Q1860 (eng)-Flame, not lame-triacontagon.wav

From Ancient Greek τρῐᾱ́κοντᾰ (trĭā́kontă) + -gon.

suffix

After projection onto the (x₁, x₂) plane, the A’s, B’s, C’s, and D’s form four concentric triacontagons, inscribed in circles of radii a, b, c, and d.

1947, H. S. M. Coxeter, Regular Polytopes, published 2012, unnumbered page:

1964 July, B. L. Chilton, On the Projection of the Regular Polytope {5, 3, 3} into a Regular Triacontagon, Canadian Mathematical Bulletin, Volume 7, Number 3, page 386,
In the projection the 600 points can be classified in 12 sets: each set consists of either of 30 or of 60 vertices which lie on a circle concentric with the outer triacontagon.

1997, Johannes Kepler, E. J. Aiton, Alistair Matheson Duncan, Judith Veronica Field (translators), The Harmony of the World, [1619, Harmonices Mundi], American Philosophical Society, Volume 309, page 59,
What should the decision now be about the sides of the Triacontagon?


deltoidal icositetrahedron

en-noun

deltoidal icositetrahedron (plural deltoidal icositetrahedra or deltoidal icositetrahedrons)

deltoidal icositetrahedra (plural)
deltoidal icositetrahedrons (plural)

These correspond to the foregoing U- and F-vertices of the deltoidal icositetrahedron whose three-edged vertices are "completely truncated"; that is to say, the truncating planes pass through the three end points of the edges radiating from the truncated vertex.

1958, The Mathematical Gazette, volume 42, page 20:

The mineral displays a well-developed habit of deltoidal icositetrahedra with dull faces.

1994, Proceedings of the Ninth Quadrennial IAGOD Symposium, International Association on the Genesis of Ore Deposits, page 593:

At the Olympus Mons Casino on Mar's they have craps games where the die are rhombic dodecahedron (12 sided), or tetrakis hexahedron (24 sides) or deltoidal icositetrahedron (24 sides). That's for your benefit, Gabby said to me.

2012, Ivan Pasztor, Of All The Things I've Lost, page 69:

(geometry) A convex polyhedron that has 24 congruent kite-shaped faces and 48 edges and is a Catalan solid, being the dual polyhedron of the rhombicuboctahedron.


truncated tetrahedron

truncated tetrahedron (plural truncated tetrahedra or truncated tetrahedrons)

truncated tetrahedra (plural)
truncated tetrahedrons (plural)

The space of the El Al pyramid is created essentially by the packing of truncated tetrahedrons.

1968, Cindy Marriott, A Critical Analysis of Israeli Architecture, 1948-1967: A Study in Cultural Conflict, page 63:

The tendons now form the edges of a slightly distorted truncated tetrahedron.

1976, Anthony Pugh, An Introduction to Tensegrity, page 35:

This ideal net gives rise to the formation of B₁₂ truncated tetrahedra, where the A cations are lodged.

2000, Angel Vegas, Cations in Inorganic Solids: Crystallography Reviews, volume 7, number 3, page 248:

2009, Xiaotian Lin, Miao Jin, Feng Luo, Xiangfen David Gu, Discrete Curvature Flows for Surfaces and 3-Manifolds, Frank Nielsen (editor), Emerging Trends in Visual Computing: LIX Fall Colloquium, ETVC 2008, page 69,
Once the edge lengths of the tetrahedral mesh have been obtained, we can realize it in the hyperbolic space ℍ³ First, we introduce how to construct a single truncated tetrahedron; then we explain how to glue multiple truncated tetrahedra by hyperbolic rigid motion.

2010, K.M. Kosuda, J. M. Bingham, K. L. Wustholz, R. P. Van Dyne, 9: Nanostructures and Surface-Enhanced Raman Spectroscopy, Gary P. Wiederrecht (efitor), Handbook of Nanoscale Optics and Electronics, page 318,
Without any further modification, the shapes of the nanoparticles fabricated by NSL are truncated tetrahedrons. However, by thermal annealing the truncated tetrahedrons are transformed into hemispheres.

(geometry) A convex polyhedron, with four triangular and four hexagonal faces, that is an Archimedean solid and can be constructed by truncating a regular tetrahedron at each vertex by one-third the length of each adjoining edge.


truncated cube

The truncation procedure that produced the truncated cube I can be applied to arbitrary polyhedra so as to obtain new polyhedra.

2003, Saul Stahl, Geometry from Euclid to Knots, published 2010, page 278:

The truncated cubes are obtained by symmetrically edging the eight vertices of the cube by l × t, where l is the length of the cubes side and 0 < t ≤ 1/2. When t = 1/2, a cuboctahedron is obtained.

2012, Cecilia Noguez, Ana L. González, “11: Localized Surface Plasmons of Multifaceted Metal Nanoparticles”, in Tapan K. Sau, Andrey L. Rogach, editors, Complex-shaped Metal Nanoparticles: Bottom-Up Syntheses and Applications, page 384:

In this subsection the optical behavior of different truncated cubes will be analyzed and compared to those of a cube and of a sphere of the same dimensions.

2013, S. D'Agostino, “Chapter 3: Size and Shape Dependence of Localized Surface Plasmon Resonances”, in Fabio Della Sala, Stefania D'Agostino, editors, Handbook of Molecular Plasmonics, page 152:

Truncated cubes can be packed sharing their octagonal faces, the remaining voids are filled by octahedra (Figure 10(b)).

2014, Walter Steurer, “1: Crystal Structures of Metallic Elements and Compounds”, in David E. Laughlin, Kazuhiro Hono, editors, Physical Metallurgy, page 20:

(geometry) A polyhedron with eight triangular and six octagonal faces that is an Archimedean solid and can be constructed by truncating a cube at each vertex along each adjoining edge.


snub dodecahedron

snub dodecahedron (plural snub dodecahedra or snub dodecahedrons)

snub dodecahedra (plural)
snub dodecahedrons (plural)

From dodecahedron simum, Kepler's name for this solid in is 1619 work Harmonices Mundi.

This gives two points, A’, A₁’, which are projections of vertices of the two enantiomorphous snub dodecahedra that can be inscribed in the regular dodecahedron.

1935, L. Lines, Solid Geometry, page 182:

The form can be derived by triangulating the pentagonal faces of the snub dodecahedron (Fig. 19).

1992, Gábor Gévay, “Icosahedral Morphology”, in István Hargittai, editor, Fivefold Symmetry, page 198:

In the case of the latter, two chiral members, the snub cube and the snub dodecahedron, are realized.

2001, Ehud Keinan, Israel Schechter, Chemistry for the 21st Century, page 138:

The snub dodecahedron has 60 vertices, 150 edges and 92 faces of which 12 are pentagonal and 80 triangular. This polyhedron has I symmetry and can therefore be constructed in left- and right-handed forms.

2006, P. W. Fowler, D. E. Manolopoulos, An Atlas of Fullerenes, page 50:

The result is a structure of two nested snub cubes rotated by an angle of 45° against each other (n = 24) and two nested snub dodecahedra, where the rotation angle amounts to 36° (n = 60).

2010, Klaus D. Sattler, editor, Handbook of Nanophysics: Clusters and Fullerenes, pages 51–8:

(geometry) A polyhedron that has 12 pentagonal and 80 triangular faces and is an Archimedean solid.

snub icosidodecahedron

polyhedron with 12 pentagonal and 80 triangular faces


great rhombicuboctahedron

great rhombicuboctahedron (plural great rhombicuboctahedra or great rhombicuboctahedrons)

great rhombicuboctahedra (plural)
great rhombicuboctahedrons (plural)

From great + rhombicuboctahedron, referring to the fact that, similarly to the rhombicuboctahedron, the 12 square faces lie in the same planes as the 12 faces of the rhombic dodecahedron, the dual of the cuboctahedron.

Figure 244 — the structure for this complicated design is the great rhombicuboctahedron, which consists of octagonal, hexagonal, and square faces.

1977, Wucius Wong, Principles of Three Dimensional Design, page 70:

Zeolite A consists of truncated octahedra flanking the edges of a larger cube; they are connected along the edges by smaller cubes, and the truncated octahedra and cubes flank a great rhombicuboctahedron at the center (28).

2005, M. Cahay, Nanoscale Devices, Materials, and Biological Systems: Fundamentals and Applications : Proceedings of the International Symposium, page 513:

The great rhombicuboctahedron can be made by truncating the cuboctahedron's vertices.

2012, Edward S. Popko, Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere, page 169:

(geometry) An Archimedean solid that is isogonal and has twenty-six regular faces (twelve square, eight hexagonal and six octagonal).

cubottaedro troncato

polyhedron with 12 square, 8 hexagonal and 6 octagonal faces


truncated cuboctahedron

truncated cuboctahedron (plural truncated cuboctahedra or truncated cuboctahedrons)

truncated cuboctahedra (plural)
truncated cuboctahedrons (plural)

From truncated + cuboctahedron, referring to a partial construction (the resultant figure needs further distortion to make the faces regular).

The H'(S-S) type of linked truncated octahedra and truncated cuboctahedra is analogous to the fluorite structure with the truncated octahedra in the positions of the fluorine atoms and the truncated cuboctahedra in the positions of the calcium atoms.

1962, The Mineralogical Magazine and Journal of the Mineralogical Society, volume 33, page 1013:

A three-dimensional network of linked cavities, each with a truncated cuboctahedron shape (Figure 6.5) through the structure, is thus formed; the truncated cuboctahedra are also space-filling (each shares its octagonal face with six others), forming channels that run parallel to the three axial cubic directions through these large cavities.

2012, Lesley E. Smart, Elaine A. Moore, Solid State Chemistry: An Introduction, 4th edition, page 274:

Its pore structure consists of truncated octahedra linked to other cavities through 6-membered rings and of truncated cuboctahedra linked together through 8-membered rings.

2013, István Palinkó, Zoltán Kónya, Ákos Kukovecz, Imre Kiricsi, “22: Zeolites”, in Robert Vajtai, editor, Springer Handbook of Nanomaterials, page 822:

great rhombicuboctahedron
great rhombicuboctahedron

(geometry) An Archimedean solid that is isogonal and has twenty-six regular faces (twelve square, eight hexagonal and six octagonal); a great rhombicuboctahedron.


геометрія

uk-noun

геоме́трія<sg>

геоме́трія • (heométrija) f inan (genitive геоме́трії, uncountable)

геоме́трія (canonical)
heométrija (romanization)
геоме́трії (genitive)
геоме́трія (nominative singular)
геоме́трії (genitive singular)
геоме́трії (dative singular)
геоме́трію (accusative singular)
геоме́трією (instrumental singular)
геоме́трії (locative singular)
геоме́тріє (singular vocative)

uk-ndecl

геоме́трія<sg>

From Ancient Greek γεωμετρία (geōmetría).