See apeirohedron in All languages combined, or Wiktionary
{ "etymology_templates": [ { "args": { "1": "en", "2": "apeiro", "3": "hedron" }, "expansion": "apeiro- + -hedron", "name": "confix" } ], "etymology_text": "From apeiro- + -hedron.", "forms": [ { "form": "apeirohedrons", "tags": [ "plural" ] }, { "form": "apeirohedra", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "s", "2": "apeirohedra" }, "expansion": "apeirohedron (plural apeirohedrons or apeirohedra)", "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": "English terms prefixed with apeiro-", "parents": [], "source": "w" }, { "kind": "other", "name": "English terms suffixed with -hedron", "parents": [], "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" }, { "kind": "other", "langcode": "en", "name": "Infinity", "orig": "en:Infinity", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "other", "langcode": "en", "name": "Non-Euclidean geometry", "orig": "en:Non-Euclidean geometry", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Polyhedra", "orig": "en:Polyhedra", "parents": [ "Shapes", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "other", "langcode": "en", "name": "Shapes in non-Euclidean geometry", "orig": "en:Shapes in non-Euclidean geometry", "parents": [], "source": "w" } ], "examples": [ { "ref": "2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:", "text": "There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.", "type": "quote" } ], "glosses": [ "A polyhedron with an infinite number of faces." ], "hyponyms": [ { "word": "mucube" }, { "word": "muoctahedron" }, { "word": "mutetrahedron" } ], "id": "en-apeirohedron-en-noun-~F3WoQdN", "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "polyhedron", "polyhedron#English" ] ], "raw_glosses": [ "(mathematics, geometry) A polyhedron with an infinite number of faces." ], "related": [ { "word": "apeirogon" } ], "topics": [ "geometry", "mathematics", "sciences" ], "wikipedia": [ "en:skew apeirohedron" ] } ], "sounds": [ { "ipa": "/əˌpiːɹɵˈhiːdɹən/" }, { "ipa": "/əˌpeɪ̯ɹɵˈhiːdɹən/" }, { "audio": "LL-Q1860 (eng)-Flame, not lame-apeirohedron.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5f/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5f/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav.ogg" } ], "word": "apeirohedron" }
{ "etymology_templates": [ { "args": { "1": "en", "2": "apeiro", "3": "hedron" }, "expansion": "apeiro- + -hedron", "name": "confix" } ], "etymology_text": "From apeiro- + -hedron.", "forms": [ { "form": "apeirohedrons", "tags": [ "plural" ] }, { "form": "apeirohedra", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "s", "2": "apeirohedra" }, "expansion": "apeirohedron (plural apeirohedrons or apeirohedra)", "name": "en-noun" } ], "hyponyms": [ { "word": "mucube" }, { "word": "muoctahedron" }, { "word": "mutetrahedron" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "apeirogon" } ], "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English nouns with irregular plurals", "English terms prefixed with apeiro-", "English terms suffixed with -hedron", "English terms with quotations", "Pages with 1 entry", "Pages with entries", "en:Geometry", "en:Infinity", "en:Mathematics", "en:Non-Euclidean geometry", "en:Polyhedra", "en:Shapes in non-Euclidean geometry" ], "examples": [ { "ref": "2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:", "text": "There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.", "type": "quote" } ], "glosses": [ "A polyhedron with an infinite number of faces." ], "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "polyhedron", "polyhedron#English" ] ], "raw_glosses": [ "(mathematics, geometry) A polyhedron with an infinite number of faces." ], "topics": [ "geometry", "mathematics", "sciences" ], "wikipedia": [ "en:skew apeirohedron" ] } ], "sounds": [ { "ipa": "/əˌpiːɹɵˈhiːdɹən/" }, { "ipa": "/əˌpeɪ̯ɹɵˈhiːdɹən/" }, { "audio": "LL-Q1860 (eng)-Flame, not lame-apeirohedron.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5f/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5f/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-apeirohedron.wav.ogg" } ], "word": "apeirohedron" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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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