polygon

From Ancient Greek πολύγωνον (polúgōnon), from πολύς (polús, “many”) + γωνία (gōnía, “angle”).

(geometry) A plane figure bounded by edges that are all straight lines.

(geometry) The boundary of such a figure.

(geometry, more generally) A figure comprising vertices and (not necessarily straight) edges, alternatingly.

(geometry) Such a figure and its interior, taken as a whole.


triangle

/ˈtɹaɪəŋɡəl/

/ˈtɹaɪˌæŋɡəl/

/ˈtɹaɪˌæŋɡəl/

PIE word
 *tréyes
From Middle English triangle, from Old French triangle, from Latin triangulum, noun use of adjective triangulus (“three-cornered, having three angles”), from trēs (“three”) + angulus (“corner, angle”), equivalent to tri- + angle.

The wedge-shaped character was the triangle, the archaic Paleolithic sign of the vulva; the pubic triangle was at the end of the phallic stylus.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 22:

(geometry) A polygon with three sides and three angles.


star

Sranan Tongo: stari
Aukan: sitali

→ Finnish: stara

→ French: star

→ German: Star

→ Italian: star

→ Swahili: staa

From Middle English sterre, from Old English steorra (“star”), from Proto-West Germanic *sterrō, variant of *sternō, from Proto-Germanic *sternô, *sternǭ (“star”), from Proto-Indo-European *h₂stḗr (“star”). Doublet of aster, stella, étoile, and estoile.
Cognates
Cognate with Scots starn, ster, North Frisian steer, West Frisian stjer, Saterland Frisian Stiern, Dutch ster, Luxembourgish Stär, German Stern, Yiddish שטערן (shtern), Vilamovian śtaom, Swedish stjärna, Norwegian stjerne, Icelandic stjarna, Gothic 𐍃𐍄𐌰𐌹𐍂𐌽𐍉 (stairnō), Spanish estrella, Portuguese estrela, Italian stella, Romanian stea, Occitan estela, Venetan stéła, Sicilian stidda, Sardinian isteddu, Mirandese streilha, Walloon sitoele, Romansch staila, Megleno-Romanian steau̯ă, Istriot stila, Istro-Romanian ste, Latin stēlla, Greek αστέρι (astéri), Ancient Greek ἀστήρ (astḗr), Old Armenian աստղ (astł), Persian ستاره (setâre), Tajik ситора (sitora), Pashto ستوری (storay), Mazanderani اساره (ëssâre), Northern Kurdish stêr, Central Kurdish ئەستێرە (estêre), Zazaki astare, Ossetian стъалы (st’aly), Hindi तारा (tārā), Urdu تارا (tārā), Punjabi ਤਾਰਾ (tārā), Gujarati તારો (tāro), Sanskrit तारा (tārā).

аеҵǝа

a celestial body appearing as a point of light on the clear night sky, whose position is relatively fixed with respect to each other

(astronomy) A spheroid of plasma with sufficient gravity to fuse hydrogen or heavier elements into heavier elements still. Depending on context the Sun may or may not be included.

نَجْم

(astronomy) a luminous celestial body made of plasma

(geometry) A concave polygon with regular, pointy protrusions and indentations, usually with four, five, or six points.

single point of failure
single point of failure

(networking) A network topology with multiple computers individually merging to one central switch, thus free of risk of collisions. A single point of failure can occur if the switch experiences corruption.


quadrilateral

Learned borrowing from Latin quadrilaterus.


square

→ Welsh: sgwâr

From Middle English square, sqware, squyre; from Old French esquarre, esquerre, (modern French équerre), from Vulgar Latin *exquadra, from Latin ex- + quadro, from quadrus (compare English quad and quadra). Doublet of squad and squadra.
Displaced fēowerecge (fēower nominative + ecg accusative, as in "four-edged").

I took refuge in the square form and exhibited a picture which consisted of nothing more than a black square on a white field.

1927, Kazimir Malevich, The Non-Objective World:

(geometry) A polygon with four straight sides of equal length and four right angles; an equilateral rectangle; a regular quadrilateral.

(roofing) A unit used in measuring roof area equivalent to 100 square feet (9.29 m²) of roof area. The materials for roofing jobs are often billed by the square in the United States.


square

en-adj

square (comparative squarer, superlative squarest)

squarer (comparative)
squarest (superlative)

The stacks had to be neat and square or the old guy grumbled and insisted on getting it just so.

The foundation has to be level and the framing has to be square.

en:ninety degree angle
en:not out of square

(of box-shaped objects such as buildings or metal frames) Forming right angles in all planes as intended; not racked or leaning.

en:ninety degree angle
en:nautical orthogonality

(nautical) Forming right angles with the mast or the keel, and parallel to the horizon; said of the yards of a square-rigged vessel when they are so braced.

Take care to make the cut completely square to the edges of the wire to give a good butt join for the ends of the wire.

2017, Julia Rai, Making Metal Clay Jewellery:

a square corner


hexagon

From Latin hexagōnum, from Ancient Greek ἑξάγωνον (hexágōnon). By surface analysis, hexa- + -gon.

(geometry) A polygon with six sides and six angles.


octagon

From Latin octagōnon, octōgōnon (“octagon”), and from its etymon Ancient Greek ὀκτάγωνον (oktágōnon, “octagon”), probably from Koine Greek ὀκτάγωνος (oktágōnos, “having eight corners”) + -ον (-on, suffix forming nouns). ὀκτάγωνος is derived from ὀκτᾰ- (okta-, prefix meaning ‘eight’) (from ὀκτώ (oktṓ, “eight”), ultimately from Proto-Indo-European *oḱtṓw (“eight”)) + γωνία (gōnía, “angle; corner”) (probably ultimately from Proto-Indo-European *ǵónu (“knee”)); analysable as octa- + -gon. The English word is cognate with Middle French octogone (modern French octogone), Italian octagono (obsolete), ottagono, Spanish octágono, octógono.
Sense 2 (“arena for mixed martial arts”) refers to its shape.

der

From the Circle deſcribe the Octagon, by taking half the Quadrant of the former for each Side of the latter. [...] [B]y conjoining theſe Points with ſtrait Lines agreeable to the Shape of the Octagon, the whole Work is completed.

1707, Andrea Pozzo, “The Ninety-second Fig. An Octangular Cupola.”, in John James, transl., Rules and Examples of Perspective Proper for Painters and Architects, etc. in English and Latin: […], London: […] Benj[amin] Motte [Sr.], […]; [s]old by John Sturt […], →OCLC:

In like manner it is demonſtrated that one angle of a regular hexagon will be equal to one right angle, and one third part of one right angle; one angle of a regular octagon equal to one right angle and half a right angle; [...]

1752, Euclid, “[Additions to the Fourth Book.] Prop[osition] VII. Probl[em]. To Describe any Regular Polygon upon a Given Right Line, Admitting the Division of a Given Arch of a Circle into any Number of Equal Parts.”, in E[dmund] Stone, transl., Euclid’s Elements of Geometry, the First Six, the Eleventh and Twelfth Books; […], London: […] Tho[mas] Payne, […], →OCLC, book IV, pages 199–200:

Bismuth is the most common of all native metallic substances. It is generally found either in cubes or octagons, or of a dendritical form, or else in thin laminæ investing the ores of other metals, particularly those of cobalt.

1808, William Nicholson, “Ores of Bismuth”, in A Dictionary of Practical and Theoretical Chemistry, […], London: […] Richard Phillips, […], →OCLC, column 2:

The font is an octagon, having at each angle a slender pillar with crockets and finials, and the sides are richly sculptured with angels and animals, the figures holding shields, with various devices; at each corner of the contracting part towards the pedestal, are cherubs heads with expanded wings; and the pedestal, which is an irregular octagon, is ornamented with four non-descript animals, scaled over their breasts; on a moulding round the bottom are several old characters, now illegible.

1810, [James Sargant Storer; John Grieg], “Worlingworth Church, Suffolk”, in Antiquarian and Topographical Cabinet, Containing a Series of Elegant Views of the Most Interesting Objects of Curiosity in Great Britain. […], volume VII, London: […] W. Clarke, […], →OCLC:

The building [the Winter Garden conservatory, Kew Gardens] was to be of five parts—a centre, two small octagons, and two wings connected by the octagons with the centre. The centre and the two octagons were finished, and some expenditure must have been laid out on the wings, as the ground was dug out and foundations in concrete laid for the pillars.

1863 June 1, [Charles William] Selwyn, “Supply—Civil Service Estimates. Supply Considered in Committee.”, in Hansard’s Parliamentary Debates, […] (House of Commons), volume CLXXI, London: Published by Cornelius Buck, at the office for “Hansard’s Parliamentary Debates,” […], →OCLC, columns 214–215:

China converted the hard octagons of the Turkoman rugs into circular scrolls or medallions, beautifying them meanwhile with floral character manifestly borrowed from the Persians and yet by no means Persian.

1922 October 28, Roy C. Bennett, “Rug Gift to National Press Club Typifies New China Industry”, in J[ohn] B[enjamin] Powell, editor, The Weekly Review, volume XXII, number 9, Shanghai: Millard Publishing Company, →OCLC, page 299, column 2:

(geometry, also attributively) A polygon with eight sides and eight angles.


undecagon

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(geometry) A polygon with eleven sides and eleven angles.


quindecagon

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(geometry) A polygon with fifteen sides and fifteen angles.


enneagon

(geometry) A polygon with nine sides; a nonagon.


heptagon

Since 16th century, from Ancient Greek ἑπτάγωνον (heptágōnon), from ἑπτά (heptá, “seven”) + γωνία (gōnía, “angle”). By surface analysis, hepta- + -gon.

A polygon with seven sides and seven angles.


dodecagon

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(geometry) A polygon with twelve edges and twelve angles.


decagon

(geometry) A polygon with ten sides and ten angles.


nonagon

(geometry) A polygon with nine sides and nine angles; an enneagon.


pentagon

From Middle French pentagone, from Late Latin pentagōnum, from Ancient Greek πεντάγωνον (pentágōnon), noun use of the neuter of the adjective πεντάγωνος (pentágōnos, “five-angled”), from πέντε (pénte, “five”) + -γωνος (-gōnos, “angled”). Equivalent to penta- + -gon.

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, […]

1884, A Square [pseudonym; Edwin A. Abbott], Flatland […] , London: Seeley & Co., Part I: This World, § 1.— Of the Nature of Flatland, page 3:

(geometry) A polygon with five sides and five angles.

pentagoon

a polygon with five sides and five angles


hendecagon

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

(geometry) A polygon with eleven edges and eleven angles.


trigon

en-noun

trigon (countable and uncountable, plural trigons)

From Ancient Greek τρίγωνον (trígōnon, “triangle”), neuter substantive of τρίγωνος (trígōnos, “three-sided”), from τρεῖς (treîs, “three”) + γωνία (gōnía, “bend, angle”). Equivalent to tri- + -gon. Doublet of trigone and trigonon.


pentagram

From Ancient Greek πεντάγραμμον (pentágrammon), noun form of the adjectives πεντάγραμμος (pentágrammos) and πεντέγραμμος (pentégrammos, “five-lined, having five lines”). Equivalent to penta- + -gram.

πεντάγραμμον

Prove that the circles so belonging to the 6 pentagrams formed by 6 lines meet in a point, and so on; the series of theorems being interminable.

1871, W. J. C. Miller, editor, Mathematical Questions and Solutions, volume XV, page 47:

The passive pentagrams of spirit are drawn first in the quarters of the passive elements—water and earth—and likewise followed by the appropriate traditional elemental pentagram.

2007, Christopher Penczak, The Temple of High Witchcraft: Ceremonies, Spheres, and the Witches' Qabalah, page 345:

Four figures involve 12 pentagrams arranged as in the faces of a dodecahedron with their vertices touching.

2012, John Barnes, Gems of Geometry, page 59:

The shape of a five-pointed star constructed of five intersecting lines meeting at the vertices, such that a central pentagon and five surrounding isosceles triangles are formed; often with magical connotations; a 5/2 (or 5/3) star polygon.


orthogon

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(trigonometry) A multi-dimensional figure in which all sides result in a right-angle, typically surpassing the restrictions of 3 dimensions.


star polygon

(geometry) A geometric figure formed by connecting, with straight lines, every vertex of a p-sided regular polygon to the qth vertex beyond it (proceeding, consistently, either clockwise or anticlockwise).


regular polygon

en-noun

regular polygon (plural regular polygons)

(geometry) A polygon which is both equiangular and equilateral (i.e. having all sides the same length and all interior angles the same).


Lemoine hexagon

Lemoine hexagon (plural Lemoine hexagons)

Named after the French mathematician Émile Lemoine.

(geometry) A cyclic hexagon with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.

Mathworld article on the Lemoine hexagon


hectogon

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(geometry) A polygon having a hundred sides.

(computing) An individual processor in some parallel processing systems.


myriagon

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For it differs in no way from the representation I should form if I were thinking of a myriagon, or any figure with very many sides.

1998, Réné Descartes, translated by Desmond M. Clarke, Meditations, Penguin, published 2003, page 58:


chiliagon

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From Ancient Greek χιλιάγωνος (khiliágōnos), from χίλιοι (khílioi, “thousand”) + γωνία (gōnía, “angle”). Equivalent to chilia- + -gon.

If Kant's claim is just that it is impossible to have a sensory experience of the absence of space, then by contrast it is not impossible to have a sensory experience of a chiliagon.

1995, Lorne Falkenstein, Kant's Intuitionism, Toronto, published 2004, page 198:

(geometry, rare) A polygon with a thousand vertices and a thousand edges.


icosagon

From Ancient Greek εἰκοσάγωνος (eikoságōnos, “having twenty sides”), from εἴκοσι (eíkosi, “twenty”) + γωνία (gōnía, “angle”). Equivalent to icosa- + -gon.

uder

1993 The upper half of a regular icosagon frame is folded. - author? - Space Structures 4

(geometry) A polygon with twenty sides and twenty angles.


heptadecagon

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The regular 17-sided polygon (heptadecagon) can be constructed with the help of a compass and a ruler.

2001, Kunihiko Kasahara, Amazing Origami, New York, N.Y.: Sterling Publishing, →ISBN:

(geometry) A polygon with seventeen sides and seventeen angles.


pentadecagon

/ˌpɛntəˈdɛkəɡən/

In ⊙ O, draw chord AB equal to r. Draw chord AC equal to Vt (which is the side of a regular decagon). CB is now one side of the regular pentadecagon.

2003, Steven Atiyah, Essentials of Geometry, Trafford, published 2003, page 357:

(geometry) A polygon with fifteen sides.


icosihenagon

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From Ancient Greek εἰκοσιέν (eikosién, “twenty-one”) + -gon.

(geometry) A polygon with twenty-one edges and twenty-one angles.


(geometry) Synonym of pentacontagon: A 50-sided polygon.


septagon

From Latin septem (“seven”) + Ancient Greek γωνία (gōnía, “angle”), equivalent to septa- + -gon.

(proscribed) A polygon with seven sides and seven angles.


henagon

From Ancient Greek: εἷς (heîs, “one”, accusative héna) + -gon.

A polygon having one edge and one angle.


triskaidecagon

A polygon having thirteen sides and thirteen angles.


tetrakaidecagon

a polygon having fourteen sides and fourteen angles


zerogon

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(geometry) A circle visualized as a polygon having no edges or vertices.


monogon

According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#x2B;2 edges, and 4s#x2B;2 faces. Of these faces, 4s#x2B;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.

1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231:

2002, Tao Li, "Laminar Branched Surfaces in 3–manifolds", Geometry & Topology 6, page 158,
There is no monogon in M-int(N(B)), ie, no disk D⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B).

a. 2006, Thilo Kuessner, "A survey on simplicial volume and invariants of foliations and laminations", in, Paweł Walczak, et al., editors, Foliations 2005, →ISBN, page 295,
An end-compressing monogon for F is a monogon properly embedded in the complimentary region C which is not homotopic (rel. boundary) into ∂C.

(geometry) A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge.


tetradecagon

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(geometry) A polygon having fourteen sides and fourteen angles.


apeirogon

/əˈpiːɹɵɡɑn/

/əˈpeɪ̯ɹɵɡɑn/

Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) apeirogon or a hypercyclic apeirogon.

1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247:

In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.

1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, →ISBN, page 27:

[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.

2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, →ISBN, page 217:

There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.

2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:

(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;

A type of generalised polygon with a countably infinite number of sides and vertices;
(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.


tridecagon

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(geometry) A polygon having thirteen sides and thirteen angles.


digon

From di- (prefix meaning ‘two’) + -gon (suffix forming the names of plane figures containing a given number of angles).

confix

monogon · digon · trigon · tetragon · pentagon · hexagon · heptagon · octagon · nonagon · decagon · undecagon · dodecagon · see also Category:English terms suffixed with -gon

They [the students] also came upon new and unusual mathematical figures: the digon, a two-sided polygon on a spherical space, and the apeirogon, an open polygon with infinitely many sides […]. All these discoveries brought up even more questions. Is a circle a polygon? What makes an octagon an octagon – its eight vertices, its eight sides, or both? Can a polygon cross itself? Does a polygon need to be closed?

2013, Brent Davis, Moshe Renert, chapter 6, in The Math Teachers Know: Profound Understanding of Emergent Mathematics, New York, N.Y., Abingdon, Oxfordshire: Routledge, →ISBN, page 102:

(geometry) A polygon having two edges and two vertices.

digono

A pair of parallel undirected edges in a multigraph.

A pair of antiparallel edges in a directed graph.


megagon

Find the constant of proportionality for a decagon, kilogon, and megagon.

1999, Mark Dugopolski, College Algebra and Trigonometry, page 505:

There can exist a regular polygon with 1000 sides (this might be called a "regular kilogon"), 1,000,000 sides (a "regular megagon"), or 1,000,000,000 sides (a "regular gigagon").

2003, Stan Gibilisco, Geometry Demystified:

A megagon is close to the perfection of a circle — a kind of generational transmutation.

2007, Arthur Greenberg, From Alchemy to Chemistry in Picture and Story:

(geometry) A polygon with one million sides.


bigon

(rare) A polygon having two edges and two vertices.


pentacontagon

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From pentaconta- (“50”) + -gon (“-sided”), from Ancient Greek πεντήκοντᾰ (pentḗkonta, “50”) and γωνία (gōnía, “corner”).


fourgon

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(geometry) A polygon with four sides; a quadrilateral.


gyrotriangle

(hyperbolic geometry) A triangle in gyrovector space.


gyroquadrilateral

(hyperbolic geometry) A quadrilateral in gyrovector space.


gyroparallelogram

The 6 faces of a parallelepiped are parallelograms while, in general, the 6 faces of a gyroparallelepiped are not gyroparallelograms.

2005, Ungar Abraham Albert, Analytic Hyperbolic Geometry:

(hyperbolic geometry) A hyperbolic quadrilateral whose two gyrodiagonals intersect at their gyromidpoints, analogous to a parallelogram in Euclidean space.


oxygon

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amblygon

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From Ancient Greek ἀμβλύς (amblús) + -gon.

(geometry, obsolete, rare) An obtuse-angled shape, especially an obtuse triangle.


surfel

(computer graphics) A unit square between voxels.


triforce

From Japanese トライフォース (toraifōsu), from English tri- + force. First used in the Legend of Zelda video game franchise for a magical artefact in that fictional universe.

A shape composed of three equilateral triangles arranged in such a manner that a fourth triangle of identical size, but pointing the opposite direction, could fit between them.

三角之力

Shape composed of three triangles in a specific alignment


heptacontagon

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(geometry) A polygon with seventy edges.


tetracontagon

Blend of tetra- (“4”) + Ancient Greek τεσσαράκοντα (tessarákonta, “40”) + -gon (“-sided”), from γωνία (gōnía, “corner”).

der

τεσσαράκοντα


Brianchon hexagon

en-noun

Brianchon hexagon (plural Brianchon hexagons)

Named after Charles Julien Brianchon (1783–1864).

(geometry) A nonplanar hexagon whose three diagonals meet.


googolgon

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(geometry) A polygon with a googol number of sides (virtually indistinguishable from a circle)


hosohedron

A tessellation of lunes on a spherical surface, such that each lune shares the same two vertices.


golygon

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(geometry) A serial isogon of 90 degrees; any polygon with all right angles, whose sides are consecutive integer lengths.


octadecagon

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A regular octadecagon cannot be constructed using a compass and straightedge.

(geometry, rare) A polygon with 18 sides and 18 vertices.


triacontagon

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From Ancient Greek τρῐᾱ́κοντᾰ (triā́konta) + -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?


hypocube

A square, or any other geometric figure analogous to a cube but having fewer than three dimensions.


hexadecagon

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(geometry) A polygon with sixteen sides and sixteen angles.


enneadecagon

(geometry) A polygon with nineteen sides and nineteen angles.


icositetragon

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(geometry) A polygon with 24 sides and 24 angles.


hexacontagon

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From Ancient Greek ἑξήκοντα (hexḗkonta, “60”) + -gon, from Ancient Greek γωνία (gōnía, “corner”).


quinquangle

/ˈkwɪŋˌkwæŋɡəl/

And from hence also shall be the geodesy of the Icosaedrum. For the finding out of the heighth of the pyramis, there is the semidiagony of the side of the decangle and the halfe ray of the circle: But the side of the decangle is a right line subtending the halfe periphery of the side of the quinquangle, or else the greater segment of the ray proportionally cut.

1636, Peter Ramus, translated by Peter Bedwell, The Way To Geometry: [Being Necessary and Usefull for Astronomers, Enginees, Geographers,. Architects, Land-meaters, Carpenters, Sea-men & Etc.], pages 277–278:

It is about 2,500 yards in circuit, is built of red stone, and, according to Von Orlich, is now " a bastioned quinquangle ; the ancient walls with semicircular bastions face the two streams ; the land side is quite regular, and consists of two bastions, and a half-bastion with three ravelins," and stands higher than any ground in face of it.

1858, Edward Thornton, A Gazetteer of the Territories Under the Government of the East India Company and of the Native States on the Continent of India, W. H. Allen & Co., page 22:

Kenett states that the military works still known by the name of Tadmarten Camp and Hook-Norton Barrow were cast up at this time ; the former, large and round, is judged to be a fortification of the Danes, and the latter, being smaller and rather a quinquangle than a square, of the Saxons.

1881, John Kirby Hedges, The history of Wallingford, volume 1, page 170:

(archaic) Synonym of pentagon, a regular 5-sided figure.


diangle

/ˈdaɪˌæŋɡəl/

The diangle ABCD indicates the entire duration of life, A and C being its commencement and its termination.

1853, “The Science of Medicine”, in The Journal of Psychological Medicine and Mental Pathology, page 241:

Now the wedge 1,2 is mapped into the exterior of the circular diangle C,S₁,1,O,2,S₂,C; both regions are indicated by a shading of the boundary. We now seek the images of the reflected wedges.

1949, Arnold Sommerfeld, translated by Ernst G. Strauss, Partial Differential Equations in Physics, volume 1, Academic Press, page 319:

Let B be a region of F bounded by a closed polygon comprised of segments of geodesics of surface F, and let hₙ be a sequence of nondegenerate diangles of region B whose sides are geodesics of region B and which converge to diangle hₙ.

1969, Siberian Mathematical Journal, Kluwer/Plenum Publishers, page 107:


biangle

/ˈbaɪˌæŋɡəl/

If n planes be drawn through any axis of the right-vector, each of which makes angles π/n with the planes on either side of it, the whole of space is divided into n congruent figures which may be called biangles, the space between any two adjacent planes being easily seen to be continuous with the vertically opposite space between them.

1895, W. Burnside, “Kinematics of Non-Euclidean Space”, in Proceedings of the Edinburgh Mathematical Society, page 46:

Then the right biangle CABD and the oblique biangle CPND are equivalent since the triangles API and BNI are congruent.

1912, Proceedings of the Edinburgh Mathematical Society, volumes 30-32, Scottish Academic Press, page 35:

It is therefore natural to consider whether precisely this concept of a straight line, with which Kant¹¹ too was familiar, is the reason why Kant in the one passage says that the concept of a straight biangle is free of contradiction.

2012 December 6, Gerold Prauss, “Kant and the Straight Biangle”, in Enno Rudolph, Ion-Olimpiu Stamatescu, editors, Philosophy, Mathematics and Modern Physics: A Dialogue, page 228:

non-Euclidean geometry
non-Euclidean geometry#English

A digon or bigon; a two-sided shape (especially in non-Euclidean geometry)


octacontagon

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

(geometry) A polygon with 80 sides and 80 angles.


enneacontagon

(geometry) A polygon with 90 sides and 90 angles.


dodecagram

A star polygon that has twelve vertices.


triacontadigon

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

(geometry) A polygon with thirty-two sides and thirty-two angles.


tetracontadigon

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

Construct an edge-to-edge tessellation with a triangle, a heptagon, and a tetracontadigon. Is it possible to continue such a tessellation to have the full petal around the tetracontadigon?

2010, Sergei Abramovich, Topics in Mathematics for Elementary Teachers, page 90:

[…] (edge-to-edge tessellation with triangle, heptagon, and tetracontadigon, see Fig. 25). Fig. 25 Edge-to-edge tessellation with triangle, heptagon, and tetracontagon

2021, Sergei Abramovich, Michael L. Connell, Developing Deep Knowledge in Middle School Mathematics:

Using GeoGebra, construct an edge-to-edge tessellation with triangle, heptagon, and tetracontadigon. Is it possible to continue such a tessellation to have the full petal around the tetracontadigon?

2024, Sergei Abramovich, Developing Deep Knowledge in Middle School Mathematics, page 82:

(geometry) A polygon with forty two sides and forty two angles.

42-угольник

сорокадвухуго́льник


dihectagon

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

Dihectagon — 200 Sides

2014, Charles W. Nigh, Geometric Shapes & Forms:

A Dihectagon is a 200 sided shape. Made using the polygon tool.

2016 February 29, Greg N., “Dihectagon”, in 3D Warehouse:

Figure 4.57 A dihectagon looks very similar to a circle. Figure 4.57 shows a 200-sided shape (a dihectagon). It looks very much like a circle now, but it isn't

2017, Ed Southall, Yes, But Why? Teaching for Understanding in Mathematics, page 90:

I understand what a hectogon (a one hundred-sided figure) is for instance, but cannot imagine one, at least not in such a way that my image would be distinct from my image of a dihectagon (see Descartes 2008 [1641]: 51-52).

2019, Kevin Lynch, “Knowing What an Experience Is Like and the Reductive Theory of Knowledge‐wh”, in Analytic Philosophy, volume 61, number 3, →DOI:

(geometry, rare) A polygon with two hundred sides and two hundred angles.

200-угольник

двухсотугольник


enneacontahexagon

Eventually, he worked his way up to a ninety-six-sided figure, an enneacontahexagon.

(geometry) A polygon with ninety six sides and ninety six angles.


icosikaidigon

The exterior wall is a 22-sided polygon (an icosikaidigon) and contains three large double-hung windows per bay.

2005, Baltimore Civil Engineering History, page 209:

A 22—sided shape once came up in relation to Activity 10.17, and various internet sources suggested we could call it an icosikaidigon!

2013, Essential Primary Mathematics, page 269:

(geometry) A polygon with twenty two sides and twenty two angles.


icosidigon

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micropolygon

(computer graphics) A very small polygon.


tetracontakaihexagon

For example, a 46-sided polygon could be called a tetracontakaihexagon, or a combination of “tetracontagon” “kai” (often used in combining names) “hexagon.”

2012, Patricia Barnes-Svarney, Thomas E Svarney, The Handy Math Answer Book, page 184:

(geometry) A polygon with forty six sides and forty six angles.


triacontakaitetragon

For instance a 34-sided polygon is called a triacontakaitetragon, and a 52-sided polygon is called a pentacontakaidigon.

2013, Mark A. Freitag, Mathematics for Elementary School Teachers, page 586:

(geometry) A polygon with thirty four sides and thirty four angles.


triacontatetragon

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


Reuleaux polygon

en-noun

Reuleaux polygon (plural Reuleaux polygons)

Named after Franz Reuleaux, 19th-century German engineer.

(geometry) A curve of constant width made up of circular arcs of constant radius.


ideal triangle

In hyperbolic geometry, a triangle whose vertices are all ideal; i.e. points at infinity, rather than real.


hyperbolic dodecahedron

hyperbolic dodecahedron (plural hyperbolic dodecahedrons)

(hyperbolic geometry) A hyperbolic version of the Euclidean dodecahedron.


planigon

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

(geometry) A convex polygon that can fill the plane with only copies of itself.


icositrigon

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

(geometry) A polygon with 23 sides and 23 angles.


Varignon parallelogram

Varignon parallelogram (plural Varignon parallelograms)

(geometry) The parallelogram involved in Varignon's theorem, whose corners are the midpoints of the sides of an arbitrary quadrilateral.


A polygon with 65537 sides and 65537 angles.


(geometry) Synonym of decagon: A polygon with ten sides and ten angles.


(geometry) Synonym of hendecagon: A polygon with eleven edges and eleven angles.


(geometry) Synonym of pentagon: A polygon with five sides and five angles.


(geometry) Synonym of octacontagon: A polygon with 80 sides and 80 angles.


(geometry, rare) Synonym of octadecagon: A polygon with 18 sides and 18 vertices.


(geometry) Synonym of enneacontagon: A polygon with 90 sides and 90 angles.


(geometry) Synonym of enneagon: A polygon with nine sides; a nonagon.


(geometry) Synonym of triacontadigon: A polygon with thirty-two sides and thirty-two angles.


(geometry, rare) Synonym of dihectagon: A polygon with two hundred sides and two hundred angles.


(geometry) Synonym of heptagon: A polygon with seven sides and seven angles.


(geometry) Synonym of icosihenagon: A polygon with twenty-one edges and twenty-one angles.


(geometry) Synonym of icosidigon: A polygon with twenty two sides and twenty two angles.


(geometry) Synonym of icositetragon: A polygon with 24 sides and 24 angles.


(geometry) Synonym of heptadecagon: A polygon with seventeen sides and seventeen angles.


(geometry) Synonym of icositrigon: A polygon with 23 sides and 23 angles.


(geometry, rare) Synonym of chiliagon: A polygon with a thousand vertices and a thousand edges.


(geometry) Synonym of hexacontagon: A 60-sided polygon.


(geometry) Synonym of hexadecagon: A polygon with sixteen sides and sixteen angles.


(geometry) Synonym of hexagon: A polygon with six sides and six angles.


(geometry) Synonym of icosagon: A polygon with twenty sides and twenty angles.


(geometry) Synonym of tetradecagon: A polygon having fourteen sides and fourteen angles.


(geometry) Synonym of tetracontagon: A 40-sided polygon.


(geometry) Synonym of triacontatetragon: A polygon with thirty four sides and thirty four angles.


(geometry) Synonym of enneadecagon: A polygon with nineteen sides and nineteen angles.


(geometry) Synonym of quadrilateral: A polygon with four sides.


(geometry) Synonym of triacontagon: A polygon with thirty sides.


(geometry) Synonym of tridecagon: A polygon having thirteen sides and thirteen angles.


(geometry) Synonym of tetracontadigon: A polygon with forty two sides and forty two angles.


(geometry) Synonym of megagon: A polygon with one million sides.


(geometry) Synonym of hectogon: A polygon having a hundred sides.


(geometry) Synonym of heptacontagon: A polygon with seventy edges.


(geometry) Synonym of enneacontahexagon: A polygon with ninety six sides and ninety six angles.


(geometry) Synonym of myriagon: A polygon with 10,000 sides.


(geometry, also attributively) Synonym of octagon: A polygon with eight sides and eight angles.


(geometry) Synonym of tetracontakaihexagon: A polygon with forty six sides and forty six angles.


(geometry) Synonym of dodecagon: A polygon with twelve edges and twelve angles.


(geometry) Synonym of pentadecagon: A polygon with fifteen sides.