See polytope in All languages combined, or Wiktionary
Download JSON data for polytope meaning in English (6.9kB)
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"etymology_text": "From German Polytop, equivalent to poly- (“many”) + -tope (“surface”). Coined by Hoppe in 1882 and introduced to English by Alicia Boole Stott.",
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"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.",
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"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.",
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{
"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.",
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"english": "generalised cube",
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{
"english": "generalised tetrahedron",
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"lang": "Catalan",
"sense": "geometric shape",
"tags": [
"masculine"
],
"word": "polítop"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "duōbāoxíng",
"sense": "geometric shape",
"word": "多胞形"
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{
"code": "eo",
"lang": "Esperanto",
"sense": "geometric shape",
"word": "hiperpluredro"
},
{
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"sense": "geometric shape",
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],
"word": "polytope"
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{
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"roman": "poritōpu",
"sense": "geometric shape",
"word": "ポリトープ"
},
{
"alt": "ちょうためんたい",
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"lang": "Japanese",
"roman": "chōtamentai",
"sense": "geometric shape",
"word": "超多面体"
},
{
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"lang": "Korean",
"roman": "dapoche",
"sense": "geometric shape",
"word": "다포체"
},
{
"code": "fa",
"lang": "Persian",
"sense": "geometric shape",
"word": "چندبر"
},
{
"code": "pl",
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"sense": "geometric shape",
"tags": [
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],
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{
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"sense": "geometric shape",
"tags": [
"masculine"
],
"word": "полиэ́др"
},
{
"code": "ru",
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"masculine"
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"word": "полито́п"
},
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"masculine"
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},
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}
],
"wikipedia": [
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"word": "polytope"
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{
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"type": "quotation"
},
{
"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": "quotation"
},
{
"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": "quotation"
}
],
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],
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],
"topics": [
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"code": "ca",
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"sense": "geometric shape",
"tags": [
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"word": "polítop"
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{
"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"
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{
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"code": "ja",
"lang": "Japanese",
"roman": "chōtamentai",
"sense": "geometric shape",
"word": "超多面体"
},
{
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"roman": "dapoche",
"sense": "geometric shape",
"word": "다포체"
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{
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"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"
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{
"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"
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{
"code": "es",
"lang": "Spanish",
"sense": "geometric shape",
"tags": [
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"word": "politopo"
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"code": "sv",
"lang": "Swedish",
"sense": "geometric shape",
"tags": [
"common-gender"
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],
"word": "polytope"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.