See 5-cell in All languages combined, or Wiktionary
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{
"ref": "1896, American Journal of Mathematics, page 181",
"text": "In every vertex of the 5-cell, 8-cell and 120-cell there are 4 concurring edges; in every vertex of the 24-cell, 8 edges.",
"type": "quotation"
},
{
"text": "1988, Unnamed translator, L. A. Sidorov, Confuguration, article in Michiel Hazewinkel (editor) Encyclopaedia of Mathematics: An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’, Volume 2: C, page 309,\nFor example, a 5-cell is bounded by five three-dimensional tetrahedra, an 8-cell by eight cubes, etc., the 5-cell and the 24-cell being duals of each other (the points correspond to spaces and lines to planes)."
},
{
"ref": "2007, Steven R. Lay, Convex Sets and Their Applications, page 230",
"text": "If we call a regular polytope with m facets an m-cell, then in E⁴ we have the 5-cell with tetrahedral facets (the simplex), the 8-cell with cubic facets (the hypercube), the 16-cell with tetrahedral facets (the regular cross-polytope), the 24-cell with octahedral facets, the 120-cell with dodecahedral facets, and the 600-cell with tetrahedral facets.",
"type": "quotation"
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"ref": "2008, Tony Robbin, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, page 16",
"text": "Later in the same document, President Hall listed all of the university's four-dimensional models: four Brill models—the 5-cell, 8-cell, 16-cell, and 24-cell—along with seven spun glass models by T. P. Hall that \"illustrated rotations.\"",
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"A four-dimensional polytope, analogous to a tetrahedron, whose five bounding facets are tetrahedra."
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"(geometry) A four-dimensional polytope, analogous to a tetrahedron, whose five bounding facets are tetrahedra."
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{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "4-simplex"
},
{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "pentachoron"
},
{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "pentahedroid"
},
{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "pentatope"
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"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "tetrahedral pyramid"
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"code": "eo",
"lang": "Esperanto",
"sense": "four-dimensional polytope analogous to a tetrahedron",
"word": "kvinĉelo"
},
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"code": "it",
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"sense": "four-dimensional polytope analogous to a tetrahedron",
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"word": "5-cella"
},
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"code": "it",
"lang": "Italian",
"sense": "four-dimensional polytope analogous to a tetrahedron",
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"masculine"
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"word": "ipertetraedro"
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"code": "it",
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"sense": "four-dimensional polytope analogous to a tetrahedron",
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"word": "pentacoro"
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"alt": "せいごほうたい",
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"roman": "seigohōtai",
"sense": "four-dimensional polytope analogous to a tetrahedron",
"word": "正五胞体"
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"text": "In every vertex of the 5-cell, 8-cell and 120-cell there are 4 concurring edges; in every vertex of the 24-cell, 8 edges.",
"type": "quotation"
},
{
"text": "1988, Unnamed translator, L. A. Sidorov, Confuguration, article in Michiel Hazewinkel (editor) Encyclopaedia of Mathematics: An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’, Volume 2: C, page 309,\nFor example, a 5-cell is bounded by five three-dimensional tetrahedra, an 8-cell by eight cubes, etc., the 5-cell and the 24-cell being duals of each other (the points correspond to spaces and lines to planes)."
},
{
"ref": "2007, Steven R. Lay, Convex Sets and Their Applications, page 230",
"text": "If we call a regular polytope with m facets an m-cell, then in E⁴ we have the 5-cell with tetrahedral facets (the simplex), the 8-cell with cubic facets (the hypercube), the 16-cell with tetrahedral facets (the regular cross-polytope), the 24-cell with octahedral facets, the 120-cell with dodecahedral facets, and the 600-cell with tetrahedral facets.",
"type": "quotation"
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"ref": "2008, Tony Robbin, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, page 16",
"text": "Later in the same document, President Hall listed all of the university's four-dimensional models: four Brill models—the 5-cell, 8-cell, 16-cell, and 24-cell—along with seven spun glass models by T. P. Hall that \"illustrated rotations.\"",
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"(geometry) A four-dimensional polytope, analogous to a tetrahedron, whose five bounding facets are tetrahedra."
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"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "4-simplex"
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{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "pentachoron"
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{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "pentahedroid"
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{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "pentatope"
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{
"sense": "4-dimensional polytope analogous to a tetrahedron",
"word": "tetrahedral pyramid"
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],
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"code": "eo",
"lang": "Esperanto",
"sense": "four-dimensional polytope analogous to a tetrahedron",
"word": "kvinĉelo"
},
{
"code": "it",
"lang": "Italian",
"sense": "four-dimensional polytope analogous to a tetrahedron",
"tags": [
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"word": "5-cella"
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"code": "it",
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"sense": "four-dimensional polytope analogous to a tetrahedron",
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"word": "ipertetraedro"
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{
"code": "it",
"lang": "Italian",
"sense": "four-dimensional polytope analogous to a tetrahedron",
"tags": [
"masculine"
],
"word": "pentacoro"
},
{
"alt": "せいごほうたい",
"code": "ja",
"lang": "Japanese",
"roman": "seigohōtai",
"sense": "four-dimensional polytope analogous to a tetrahedron",
"word": "正五胞体"
}
],
"word": "5-cell"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-06 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 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.
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