See 24-cell in All languages combined, or Wiktionary
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"ref": "1995, Harold Scott Macdonald Coxeter, “Paper Three: Two Aspects of the Regular 24-Cell in Four Dimensions”, in F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Iviċ Weiss, editors, Kaleidoscopes: Selected Writings of H.S.M. Coxeter, page 25",
"text": "The octagonal projection of the regular 24-cell {3,4,3} reveals that the 24 vertices of this 4-dimensional polytope can be distributed as 16 + 8: the 16 vertices of the 4-cube γ₄ = {4,3,3} and the 8 vertices of its dual, the 16-cell β₄ = {3,3,4}. This view of the 24-cell is less well-known than the dodecagonal projection, in which the β₄ appears as two squares of different sizes joined by 8 equilateral triangles.",
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"text": "2002, T. Robbin, Formian for art and mathematics, G. A. R. Parke, P. Disney (editors), Space Structures 5, Proceedings of the 5th International Conference on Space Structures, Volume 1, page 445,\nOne more example of a four dimensional tessellation is given using the 24-cell, see Fig 2."
},
{
"ref": "2002, Gabor Toth, Glimpses of Algebra and Geometry, 2nd edition, page 385",
"text": "The regular polytope with Schläfli symbol {3,4,3}, the so-called 24-cell, can be obtained from the 16-cell as follows. The vertices of the 24-cell are the midpoints of the 24 edges of the 16-cell.",
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"A four-dimensional polytope whose twenty-four bounding facets are octahedra and which has no three-dimensional analogue."
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"(geometry) A four-dimensional polytope whose twenty-four bounding facets are octahedra and which has no three-dimensional analogue."
],
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{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "hyper-diamond"
},
{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "icositetrachoron"
},
{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "octacube"
},
{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "octaplex"
},
{
"sense": "4-dimensional polytope with 24 octahedral facets",
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"translations": [
{
"code": "eo",
"lang": "Esperanto",
"sense": "four-dimensional polytope",
"word": "dudekkvarĉelo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "four-dimensional polytope",
"word": "24-solu"
},
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"alt": "せいにじゅうしほうたい",
"code": "ja",
"lang": "Japanese",
"roman": "seinijūshihōtai",
"sense": "four-dimensional polytope",
"word": "正二十四胞体"
}
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"ipa": "/twɛntiˈfoʊɹˌsɛl/"
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"word": "24-cell"
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"ref": "1995, Harold Scott Macdonald Coxeter, “Paper Three: Two Aspects of the Regular 24-Cell in Four Dimensions”, in F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Iviċ Weiss, editors, Kaleidoscopes: Selected Writings of H.S.M. Coxeter, page 25",
"text": "The octagonal projection of the regular 24-cell {3,4,3} reveals that the 24 vertices of this 4-dimensional polytope can be distributed as 16 + 8: the 16 vertices of the 4-cube γ₄ = {4,3,3} and the 8 vertices of its dual, the 16-cell β₄ = {3,3,4}. This view of the 24-cell is less well-known than the dodecagonal projection, in which the β₄ appears as two squares of different sizes joined by 8 equilateral triangles.",
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"text": "2002, T. Robbin, Formian for art and mathematics, G. A. R. Parke, P. Disney (editors), Space Structures 5, Proceedings of the 5th International Conference on Space Structures, Volume 1, page 445,\nOne more example of a four dimensional tessellation is given using the 24-cell, see Fig 2."
},
{
"ref": "2002, Gabor Toth, Glimpses of Algebra and Geometry, 2nd edition, page 385",
"text": "The regular polytope with Schläfli symbol {3,4,3}, the so-called 24-cell, can be obtained from the 16-cell as follows. The vertices of the 24-cell are the midpoints of the 24 edges of the 16-cell.",
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{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "hyper-diamond"
},
{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "icositetrachoron"
},
{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "octacube"
},
{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "octaplex"
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{
"sense": "4-dimensional polytope with 24 octahedral facets",
"word": "polyoctahedron"
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"code": "eo",
"lang": "Esperanto",
"sense": "four-dimensional polytope",
"word": "dudekkvarĉelo"
},
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"lang": "Finnish",
"sense": "four-dimensional polytope",
"word": "24-solu"
},
{
"alt": "せいにじゅうしほうたい",
"code": "ja",
"lang": "Japanese",
"roman": "seinijūshihōtai",
"sense": "four-dimensional polytope",
"word": "正二十四胞体"
}
],
"word": "24-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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