See polytope in All languages combined, or Wiktionary
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Pierrot, M. Benoit, P. Dauchez, “SamoS: A Pythagorean Solution for Omnidirectional Underwater Vehicles”, in Jadran Lenar I, Manfred L. Husty, editors, Advances in Robot Kinematics: Analysis and Control, page 220:", "text": "This polytope is mapped into a Cartesian force polytope (resp. torque polytope) in the Cartesian space. Such a polytope represents the exact force (resp. torque) that can be produced on the vehicle main body.", "type": "quote" }, { "ref": "2006, Rekha R. Thomas, Lectures in Geometric Combinatorics, page 27:", "text": "Verify the Hirsch conjecture for the 3-cube, 4-cube and any other polytope that takes your fancy.\nThe Steinitz theorem is a very satisfactory understanding of the graphs of three-dimensional polytopes.", "type": "quote" } ], "glosses": [ "A finite region of n-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence \"point, line segment, polygon, polyhedron, ...\"." ], "hyponyms": [ { "sense": "geometrical figure", "word": "polygon (2D figure)" }, { "sense": "geometrical figure", "word": "polyhedron (3D figure)" }, { "sense": "geometrical figure", "word": "polychoron (4D figure)" }, { "english": "generalised cube", "sense": "geometrical figure", "word": "hypercube" }, { "english": "generalised tetrahedron", "sense": "geometrical figure", "word": "simplex" }, { "sense": "geometrical figure", "word": "tesseract (4D cube)" } ], "id": "en-polytope-en-noun-MmBUObOY", "links": [ [ "geometry", "geometry" ], [ "finite", "finite" ], [ "dimensional", "dimensional" ], [ "bound", "bound" ], [ "hyperplane", "hyperplane" ], [ "geometrical", "geometrical" ], [ "sequence", "sequence" ], [ "point", "point" ], [ "line segment", "line segment" ], [ "polygon", "polygon" ], [ "polyhedron", "polyhedron" ] ], "raw_glosses": [ "(geometry) A finite region of n-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence \"point, line segment, polygon, polyhedron, ...\"." ], "related": [ { "word": "polytopic" } ], "topics": [ "geometry", "mathematics", "sciences" ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "geometric shape", "tags": [ "masculine" ], "word": "polítop" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "duōbāoxíng", "sense": "geometric shape", "word": "多胞形" }, { "code": "eo", "lang": "Esperanto", "sense": "geometric shape", "word": "hiperpluredro" }, { "code": "fr", "lang": "French", "sense": "geometric shape", "tags": [ "masculine" ], "word": "polytope" }, { "code": "de", "lang": "German", "sense": "geometric shape", "tags": [ "masculine" ], "word": "Polytop" }, { "code": "hu", "lang": "Hungarian", "sense": "geometric shape", "word": "politóp" }, { "code": "it", "lang": "Italian", "sense": "geometric shape", "tags": [ "masculine" ], "word": "politopo" }, { "code": "ja", "lang": "Japanese", "roman": "poritōpu", "sense": "geometric shape", "word": "ポリトープ" }, { "alt": "ちょうためんたい", "code": "ja", "lang": "Japanese", "roman": "chōtamentai", "sense": "geometric shape", "word": "超多面体" }, { "alt": "多胞體", "code": "ko", "lang": "Korean", "roman": "dapoche", "sense": "geometric shape", "word": "다포체" }, { "code": "fa", "lang": "Persian", "sense": "geometric shape", "word": "چندبر" }, { "code": "pl", "lang": "Polish", "sense": "geometric shape", "tags": [ "masculine" ], "word": "wielotop" }, { "code": "pl", "lang": "Polish", "sense": "geometric shape", "tags": [ "feminine" ], "word": "wielokomórka" }, { "code": "pt", "lang": "Portuguese", "sense": "geometric shape", "tags": [ "masculine" ], "word": "politopo" }, { "code": "ru", "lang": "Russian", "roman": "poliédr", "sense": "geometric shape", "tags": [ "masculine" ], "word": "полиэ́др" }, { "code": "ru", "lang": "Russian", "roman": "politóp", "sense": "geometric shape", "tags": [ "masculine" ], "word": "полито́п" }, { "code": "es", "lang": "Spanish", "sense": "geometric shape", "tags": [ "masculine" ], "word": "politopo" }, { "code": "sv", "lang": "Swedish", "sense": "geometric shape", "tags": [ "common-gender" ], "word": "polytop" } ], "wikipedia": [ "polytope" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Flame, not lame-polytope.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/57/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/57/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav.ogg" } ], "word": "polytope" }
{ "derived": [ { "word": "4-polytope" }, { "word": "cross-polytope" } ], "etymology_templates": [ { "args": { "1": "en", "2": "de", "3": "Polytop" }, "expansion": "German Polytop", "name": "uder" } ], "etymology_text": "From German Polytop, equivalent to poly- (“many”) + -tope (“surface”). Coined by Hoppe in 1882 and introduced to English by Alicia Boole Stott.", "forms": [ { "form": "polytopes", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "polytope (plural polytopes)", "name": "en-noun" } ], "hyponyms": [ { "sense": "geometrical figure", "word": "polygon (2D figure)" }, { "sense": "geometrical figure", "word": "polyhedron (3D figure)" }, { "sense": "geometrical figure", "word": "polychoron (4D figure)" }, { "english": "generalised cube", "sense": "geometrical figure", "word": "hypercube" }, { "english": "generalised tetrahedron", "sense": "geometrical figure", "word": "simplex" }, { "sense": "geometrical figure", "word": "tesseract (4D cube)" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "polytopic" } ], "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms derived from German", "English terms with quotations", "English undefined derivations", "Entries with translation boxes", "Japanese terms with redundant script codes", "Mandarin terms with redundant transliterations", "Pages with 2 entries", "Pages with entries", "Terms with Catalan translations", "Terms with Esperanto translations", "Terms with French translations", "Terms with German translations", "Terms with Hungarian translations", "Terms with Italian translations", "Terms with Japanese translations", "Terms with Korean translations", "Terms with Mandarin translations", "Terms with Persian translations", "Terms with Polish translations", "Terms with Portuguese translations", "Terms with Russian translations", "Terms with Spanish translations", "Terms with Swedish translations", "en:Geometry", "en:Higher-dimensional geometry", "en:Shapes" ], "examples": [ { "ref": "1964, Victor Klee, On the Number of Vertices of a Convex Polytope: Canadian Journal of Mathematics, volume XVI, number 4, page 701:", "text": "As is well known, the theory of linear inequalities is closely related to the study of convex polytopes.", "type": "quote" }, { "ref": "1998, F. Pierrot, M. Benoit, P. Dauchez, “SamoS: A Pythagorean Solution for Omnidirectional Underwater Vehicles”, in Jadran Lenar I, Manfred L. Husty, editors, Advances in Robot Kinematics: Analysis and Control, page 220:", "text": "This polytope is mapped into a Cartesian force polytope (resp. torque polytope) in the Cartesian space. Such a polytope represents the exact force (resp. torque) that can be produced on the vehicle main body.", "type": "quote" }, { "ref": "2006, Rekha R. Thomas, Lectures in Geometric Combinatorics, page 27:", "text": "Verify the Hirsch conjecture for the 3-cube, 4-cube and any other polytope that takes your fancy.\nThe Steinitz theorem is a very satisfactory understanding of the graphs of three-dimensional polytopes.", "type": "quote" } ], "glosses": [ "A finite region of n-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence \"point, line segment, polygon, polyhedron, ...\"." ], "links": [ [ "geometry", "geometry" ], [ "finite", "finite" ], [ "dimensional", "dimensional" ], [ "bound", "bound" ], [ "hyperplane", "hyperplane" ], [ "geometrical", "geometrical" ], [ "sequence", "sequence" ], [ "point", "point" ], [ "line segment", "line segment" ], [ "polygon", "polygon" ], [ "polyhedron", "polyhedron" ] ], "raw_glosses": [ "(geometry) A finite region of n-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence \"point, line segment, polygon, polyhedron, ...\"." ], "topics": [ "geometry", "mathematics", "sciences" ], "wikipedia": [ "polytope" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Flame, not lame-polytope.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/57/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/57/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-polytope.wav.ogg" } ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "geometric shape", "tags": [ "masculine" ], "word": "polítop" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "duōbāoxíng", "sense": "geometric shape", "word": "多胞形" }, { "code": "eo", "lang": "Esperanto", "sense": "geometric shape", "word": "hiperpluredro" }, { "code": "fr", "lang": "French", "sense": "geometric shape", "tags": [ "masculine" ], "word": "polytope" }, { "code": "de", "lang": "German", "sense": "geometric shape", "tags": [ "masculine" ], "word": "Polytop" }, { "code": "hu", "lang": "Hungarian", "sense": "geometric shape", "word": "politóp" }, { "code": "it", "lang": "Italian", "sense": "geometric shape", "tags": [ "masculine" ], "word": "politopo" }, { "code": "ja", "lang": "Japanese", "roman": "poritōpu", "sense": "geometric shape", "word": "ポリトープ" }, { "alt": "ちょうためんたい", "code": "ja", "lang": "Japanese", "roman": "chōtamentai", "sense": "geometric shape", "word": "超多面体" }, { "alt": "多胞體", "code": "ko", "lang": "Korean", "roman": "dapoche", "sense": "geometric shape", "word": "다포체" }, { "code": "fa", "lang": "Persian", "sense": "geometric shape", "word": "چندبر" }, { "code": "pl", "lang": "Polish", "sense": "geometric shape", "tags": [ "masculine" ], "word": "wielotop" }, { "code": "pl", "lang": "Polish", "sense": "geometric shape", "tags": [ "feminine" ], "word": "wielokomórka" }, { "code": "pt", "lang": "Portuguese", "sense": "geometric shape", "tags": [ "masculine" ], "word": "politopo" }, { "code": "ru", "lang": "Russian", "roman": "poliédr", "sense": "geometric shape", "tags": [ "masculine" ], "word": "полиэ́др" }, { "code": "ru", "lang": "Russian", "roman": "politóp", "sense": "geometric shape", "tags": [ "masculine" ], "word": "полито́п" }, { "code": "es", "lang": "Spanish", "sense": "geometric shape", "tags": [ "masculine" ], "word": "politopo" }, { "code": "sv", "lang": "Swedish", "sense": "geometric shape", "tags": [ "common-gender" ], "word": "polytop" } ], "word": "polytope" }
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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 2025-02-26 from the enwiktionary dump dated 2025-02-21 using wiktextract (ce0be54 and f2e72e5). 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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