See Schläfli symbol on Wiktionary
{
"etymology_text": "From Schläfli (“a surname”) + symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895).",
"forms": [
{
"form": "Schläfli symbols",
"tags": [
"plural"
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{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
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"Formal sciences",
"Sciences",
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"Fundamental"
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"source": "w"
},
{
"kind": "topical",
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"name": "Higher-dimensional geometry",
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"name": "Tesselation",
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"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": "quote"
},
{
"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": "quote"
}
],
"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_text": "From Schläfli (“a surname”) + symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895).",
"forms": [
{
"form": "Schläfli symbols",
"tags": [
"plural"
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"en:Geometry",
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"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": "quote"
},
{
"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": "quote"
}
],
"glosses": [
"A notation that recursively encodes certain properties of a specified regular polytope or tessellation."
],
"links": [
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"geometry",
"geometry"
],
[
"regular",
"regular"
],
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"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"
}
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-01-13 from the enwiktionary dump dated 2025-01-01 using wiktextract (4ba5975 and 4ed51a5). 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.
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