See orthoplex on Wiktionary
{ "etymology_templates": [ { "args": { "1": "en", "2": "orthant", "3": "complex" }, "expansion": "Blend of orthant + complex", "name": "blend" } ], "etymology_text": "Coined in 1991 by John Horton Conway and Neil Sloane. Blend of orthant + complex, since it has one facet for each orthant.", "forms": [ { "form": "orthoplexes", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "orthoplex (plural orthoplexes)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English blends", "parents": [], "source": "w" }, { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Geometry", "orig": "en:Geometry", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "derived": [ { "word": "4-orthoplex" } ], "examples": [ { "ref": "1990, Mathematica Journal, volumes 1-2, page 84:", "text": "We made use of another way of considering the 120 cells, starting with the eight at the vertices of an orthoplex, that is, in the cells of a hypercube.", "type": "quote" }, { "ref": "1991, J. H. Conway, N. J. A. Sloane, “The Cell Structures of Certain Lattices”, in Peter Hilton, Friedrich Hirzebruch, Reinhold Remmert, editors, Miscellanea Mathematica, page 90:", "text": "It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.", "type": "quote" }, { "ref": "2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 412:", "text": "The combinatorics of this case apply to all members of the Gosset series; in every case, their cells are simplexes and orthoplexes, the latter appearing with only half symmetry.", "type": "quote" } ], "glosses": [ "A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions)." ], "hyponyms": [ { "sense": "polytope analogous to an octahedron", "word": "16-cell" }, { "sense": "polytope analogous to an octahedron", "word": "4-orthoplex" }, { "sense": "polytope analogous to an octahedron", "word": "hexadecachoron" }, { "sense": "polytope analogous to an octahedron", "word": "octahedron" } ], "id": "en-orthoplex-en-noun-Gx30JkkF", "links": [ [ "geometry", "geometry" ], [ "convex", "convex" ], [ "polytope", "polytope" ], [ "octahedron", "octahedron" ], [ "16-cell", "16-cell" ] ], "raw_glosses": [ "(geometry) A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions)." ], "related": [ { "word": "simplex" }, { "word": "hypercube" }, { "word": "Turán graph" } ], "synonyms": [ { "sense": "polytope analogous to an octahedron", "word": "cocube" }, { "sense": "polytope analogous to an octahedron", "word": "cross-polytope" }, { "sense": "polytope analogous to an octahedron", "word": "hyperoctahedron" } ], "topics": [ "geometry", "mathematics", "sciences" ], "wikipedia": [ "Cross-polytope", "John Horton Conway", "Neil Sloane" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Flame, not lame-orthoplex.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/aa/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/aa/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav.ogg" } ], "word": "orthoplex" }
{ "derived": [ { "word": "4-orthoplex" } ], "etymology_templates": [ { "args": { "1": "en", "2": "orthant", "3": "complex" }, "expansion": "Blend of orthant + complex", "name": "blend" } ], "etymology_text": "Coined in 1991 by John Horton Conway and Neil Sloane. Blend of orthant + complex, since it has one facet for each orthant.", "forms": [ { "form": "orthoplexes", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "orthoplex (plural orthoplexes)", "name": "en-noun" } ], "hyponyms": [ { "sense": "polytope analogous to an octahedron", "word": "16-cell" }, { "sense": "polytope analogous to an octahedron", "word": "4-orthoplex" }, { "sense": "polytope analogous to an octahedron", "word": "hexadecachoron" }, { "sense": "polytope analogous to an octahedron", "word": "octahedron" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "simplex" }, { "word": "hypercube" }, { "word": "Turán graph" } ], "senses": [ { "categories": [ "English blends", "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms with quotations", "Pages with 1 entry", "Pages with entries", "en:Geometry" ], "examples": [ { "ref": "1990, Mathematica Journal, volumes 1-2, page 84:", "text": "We made use of another way of considering the 120 cells, starting with the eight at the vertices of an orthoplex, that is, in the cells of a hypercube.", "type": "quote" }, { "ref": "1991, J. H. Conway, N. J. A. Sloane, “The Cell Structures of Certain Lattices”, in Peter Hilton, Friedrich Hirzebruch, Reinhold Remmert, editors, Miscellanea Mathematica, page 90:", "text": "It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.", "type": "quote" }, { "ref": "2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 412:", "text": "The combinatorics of this case apply to all members of the Gosset series; in every case, their cells are simplexes and orthoplexes, the latter appearing with only half symmetry.", "type": "quote" } ], "glosses": [ "A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions)." ], "links": [ [ "geometry", "geometry" ], [ "convex", "convex" ], [ "polytope", "polytope" ], [ "octahedron", "octahedron" ], [ "16-cell", "16-cell" ] ], "raw_glosses": [ "(geometry) A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions)." ], "topics": [ "geometry", "mathematics", "sciences" ], "wikipedia": [ "Cross-polytope", "John Horton Conway", "Neil Sloane" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Flame, not lame-orthoplex.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/aa/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/aa/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-orthoplex.wav.ogg" } ], "synonyms": [ { "sense": "polytope analogous to an octahedron", "word": "cocube" }, { "sense": "polytope analogous to an octahedron", "word": "cross-polytope" }, { "sense": "polytope analogous to an octahedron", "word": "hyperoctahedron" } ], "word": "orthoplex" }
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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 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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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