See 4-polytope on Wiktionary
{ "etymology_text": "From 4-dimensional + polytope.", "forms": [ { "form": "4-polytopes", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "4-polytope (plural 4-polytopes)", "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": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian 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" } ], "examples": [ { "ref": "1984, London Mathematical Society lecture note series, numbers 88-90, page 101:", "text": "Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence.", "type": "quote" }, { "ref": "2004, Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler, “16: Basic properties of convex polytopes”, in Joseph O'Rourke, Jacob E. Goodman, editors, Handbook of Discrete and Computational Geometry, 2nd edition, page 369:", "text": "The situation for 4-polytopes is fundamentally different from that for 3-dimensional polytopes. One reason is that there is no similar reduction of 4-polytope theory to a combinatorial (graph) problem.", "type": "quote" }, { "ref": "2011, Felix Effenberger, Hamiltonian Submanifolds of Regular Polytopes, page 40:", "text": "For d = 4, Hamiltonian cycles in the regular 4-polytopes are known to exist. However, it seems that so far no decision about the existence or non-existence of 1-Hamiltonian surfaces in the 2-skeleton of any of the three sporadic regular 4-polytopes can be made, compare [120].", "type": "quote" } ], "glosses": [ "A four-dimensional polytope." ], "id": "en-4-polytope-en-noun-FesFp0NZ", "links": [ [ "geometry", "geometry" ], [ "four-dimensional", "four-dimensional" ], [ "polytope", "polytope" ] ], "raw_glosses": [ "(geometry) A four-dimensional polytope." ], "synonyms": [ { "sense": "4-dimensional polytope", "word": "polycell" }, { "sense": "4-dimensional polytope", "word": "polychoron" }, { "sense": "4-dimensional polytope", "word": "polyhedroid" } ], "topics": [ "geometry", "mathematics", "sciences" ], "translations": [ { "code": "it", "lang": "Italian", "sense": "4-dimensional polytope", "tags": [ "masculine" ], "word": "policoro" } ], "wikipedia": [ "4-polytope" ] } ], "word": "4-polytope" }
{ "etymology_text": "From 4-dimensional + polytope.", "forms": [ { "form": "4-polytopes", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "4-polytope (plural 4-polytopes)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "English terms spelled with numbers", "English terms with quotations", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Quotation templates to be cleaned", "Terms with Italian translations", "en:Geometry", "en:Higher-dimensional geometry" ], "examples": [ { "ref": "1984, London Mathematical Society lecture note series, numbers 88-90, page 101:", "text": "Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence.", "type": "quote" }, { "ref": "2004, Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler, “16: Basic properties of convex polytopes”, in Joseph O'Rourke, Jacob E. Goodman, editors, Handbook of Discrete and Computational Geometry, 2nd edition, page 369:", "text": "The situation for 4-polytopes is fundamentally different from that for 3-dimensional polytopes. One reason is that there is no similar reduction of 4-polytope theory to a combinatorial (graph) problem.", "type": "quote" }, { "ref": "2011, Felix Effenberger, Hamiltonian Submanifolds of Regular Polytopes, page 40:", "text": "For d = 4, Hamiltonian cycles in the regular 4-polytopes are known to exist. However, it seems that so far no decision about the existence or non-existence of 1-Hamiltonian surfaces in the 2-skeleton of any of the three sporadic regular 4-polytopes can be made, compare [120].", "type": "quote" } ], "glosses": [ "A four-dimensional polytope." ], "links": [ [ "geometry", "geometry" ], [ "four-dimensional", "four-dimensional" ], [ "polytope", "polytope" ] ], "raw_glosses": [ "(geometry) A four-dimensional polytope." ], "topics": [ "geometry", "mathematics", "sciences" ], "wikipedia": [ "4-polytope" ] } ], "synonyms": [ { "sense": "4-dimensional polytope", "word": "polycell" }, { "sense": "4-dimensional polytope", "word": "polychoron" }, { "sense": "4-dimensional polytope", "word": "polyhedroid" } ], "translations": [ { "code": "it", "lang": "Italian", "sense": "4-dimensional polytope", "tags": [ "masculine" ], "word": "policoro" } ], "word": "4-polytope" }
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