See Schläfli symbol in All languages combined, or Wiktionary
Download JSON data for Schläfli symbol meaning in English (5.0kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "Schläfli",
"3": "",
"4": "a surname"
},
"expansion": "Schläfli (“a surname”)",
"name": "m"
},
{
"args": {
"1": "en",
"2": "symbol"
},
"expansion": "symbol",
"name": "m"
}
],
"etymology_text": "From Schläfli (“a surname”) + symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895).",
"forms": [
{
"form": "Schläfli symbols",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Schläfli symbol (plural Schläfli symbols)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English entries with language name categories using raw markup",
"parents": [
"Entries with language name categories using raw markup",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms with non-redundant non-automated sortkeys",
"parents": [
"Terms with non-redundant non-automated sortkeys",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Romanian unattested translations",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Higher-dimensional geometry",
"orig": "en:Higher-dimensional geometry",
"parents": [
"Geometry",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Tesselation",
"orig": "en:Tesselation",
"parents": [],
"source": "w"
}
],
"examples": [
{
"text": "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,\nThe 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}."
},
{
"ref": "2007, Michael E. Mortenson, chapter L, in Geometric Transformations for 3D Modeling, page 248",
"text": "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.",
"type": "quotation"
},
{
"ref": "2012, John Barnes, Gems of Geometry, 2nd edition, page 79",
"text": "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.",
"type": "quotation"
}
],
"glosses": [
"A notation that recursively encodes certain properties of a specified regular polytope or tessellation."
],
"id": "en-Schläfli_symbol-en-noun-NcRRDKbo",
"links": [
[
"geometry",
"geometry"
],
[
"regular",
"regular"
],
[
"polytope",
"polytope"
],
[
"tessellation",
"tessellation"
]
],
"raw_glosses": [
"(geometry) A notation that recursively encodes certain properties of a specified regular polytope or tessellation."
],
"synonyms": [
{
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "Schläfli notation"
}
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "Schläflin symboli"
},
{
"code": "de",
"lang": "German",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"tags": [
"neuter"
],
"word": "Schläfli-Symbol"
},
{
"code": "it",
"lang": "Italian",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"tags": [
"masculine"
],
"word": "simbolo di Schläfli"
},
{
"alt": "シュレーフリきごう",
"code": "ja",
"lang": "Japanese",
"roman": "Shurēfuri kigō",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "シュレーフリ記号"
},
{
"code": "ko",
"lang": "Korean",
"roman": "syullaepeulli giho",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "슐래플리 기호"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "no attested term in Romanian"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"tags": [
"neuter"
],
"word": "but see simbol Schläfli"
}
],
"wikipedia": [
"Ludwig Schläfli",
"Schläfli symbol"
]
}
],
"word": "Schläfli symbol"
}
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "Schläfli",
"3": "",
"4": "a surname"
},
"expansion": "Schläfli (“a surname”)",
"name": "m"
},
{
"args": {
"1": "en",
"2": "symbol"
},
"expansion": "symbol",
"name": "m"
}
],
"etymology_text": "From Schläfli (“a surname”) + symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895).",
"forms": [
{
"form": "Schläfli symbols",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Schläfli symbol (plural Schläfli symbols)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with language name categories using raw markup",
"English entries with topic categories using raw markup",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms spelled with Ä",
"English terms spelled with ◌̈",
"English terms with non-redundant non-automated sortkeys",
"English terms with quotations",
"Quotation templates to be cleaned",
"Romanian unattested translations",
"en:Geometry",
"en:Higher-dimensional geometry",
"en:Tesselation"
],
"examples": [
{
"text": "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,\nThe 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}."
},
{
"ref": "2007, Michael E. Mortenson, chapter L, in Geometric Transformations for 3D Modeling, page 248",
"text": "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.",
"type": "quotation"
},
{
"ref": "2012, John Barnes, Gems of Geometry, 2nd edition, page 79",
"text": "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.",
"type": "quotation"
}
],
"glosses": [
"A notation that recursively encodes certain properties of a specified regular polytope or tessellation."
],
"links": [
[
"geometry",
"geometry"
],
[
"regular",
"regular"
],
[
"polytope",
"polytope"
],
[
"tessellation",
"tessellation"
]
],
"raw_glosses": [
"(geometry) A notation that recursively encodes certain properties of a specified regular polytope or tessellation."
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
"wikipedia": [
"Ludwig Schläfli",
"Schläfli symbol"
]
}
],
"synonyms": [
{
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "Schläfli notation"
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "Schläflin symboli"
},
{
"code": "de",
"lang": "German",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"tags": [
"neuter"
],
"word": "Schläfli-Symbol"
},
{
"code": "it",
"lang": "Italian",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"tags": [
"masculine"
],
"word": "simbolo di Schläfli"
},
{
"alt": "シュレーフリきごう",
"code": "ja",
"lang": "Japanese",
"roman": "Shurēfuri kigō",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "シュレーフリ記号"
},
{
"code": "ko",
"lang": "Korean",
"roman": "syullaepeulli giho",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "슐래플리 기호"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"word": "no attested term in Romanian"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "notation encoding certain properties of a regular polytope or tessellation",
"tags": [
"neuter"
],
"word": "but see simbol Schläfli"
}
],
"word": "Schläfli symbol"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.