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Statements

Subject Item
dbr:Uniform_polyhedron
rdfs:label
均勻多面體 Poliedro uniforme Polyèdre uniforme Uniform polyhedron Poliedro uniforme 고른 다면체 Poliedro uniforme 一様多面体 Políedre uniforme Unuforma pluredro
rdfs:comment
In geometria, un poliedro uniforme è un poliedro che ammette molte simmetrie, le cui facce sono poligoni regolari e i cui vertici sono omogenei. Le facce non devono però essere necessariamente convesse: molti poliedri uniformi sono quindi stellati. Unuforma pluredro estas unuforma hiperpluredro, 3-dimensia pluredro kiu havas regulaj plurlateroj kiel edroj kaj estas vertico-transitiva. Ĉiuj ĝiaj verticoj estas , kaj la pluredro havas altan gradon de reflekta kaj turna simetrio. Unuformaj pluredroj povas esti regula, kvazaŭregula aŭ duonregula. La edroj kaj verticoj ne nepre esta konveksaj, inter unuformaj pluredroj estas ankaŭ . Malinkluzivante la malfiniajn arojn estas 75 unuformaj pluredroj (aŭ 76 se al lateroj estas permesite koincidi). La kategorioj inkluzivas: 在幾何學中,均勻多面體是指由正多邊形面構成且具有頂點可遞特性的多面體,點可遞代表該幾何結構中的任2個頂點其中一個頂點可以透過平移、旋轉與鏡射的過程映射到另一個頂點,換句話說這個幾何結構的頂角是全等的,所以該多面體具有具有高度鏡射和旋轉對稱。 均勻多面體可能是正多面體(同時具備面可遞、邊可遞)、擬正多面體(若邊可遞,則面不可遞)或半正多面體(邊未必可遞面也未必可遞)。由於面和頂角不一定要是凸的,所以很多均勻多面體的也是星狀多面體。 不包括無限集合,有75個均勻多面體(如果允許邊緣重合則有76種)。 * 凸多面體 * 5種凸正多面體 * 13種阿基米德立體——兩種擬正多面體和11種半正多面體 * 星狀多面體 * 4種克卜勒-龐索立體——正非凸多面體 * 53種均勻星形多面體——5種擬正多面體和48種半正多面體 * 1種由約翰·斯基林發現與對邊重合的星狀多面體,稱為大二重扭稜二重斜方十二面體或斯基林圖形(Skilling's figure)。 En geometria, un políedre uniforme és un políedre que admet moltes simetries, les seves cares són polígons regulars i els seus vèrtex són homogenis. Però les cares no cal que siguin per força polígons convexos: per tant, molts polígons uniformes són estelats. Vegeu també: Llista de políedres uniformes Un poliedro uniforme es una figura tridimensional que tiene polígonos regulares como caras y es isogonal (es decir, presenta una isometría que permite hacer corresponder el conjunto de sus vértices entre sí mediante relaciones de simetría). De ello se deduce que todos sus vértices son congruentes.​ Hay dos clases infinitas de poliedros uniformes, junto con otros 75 poliedros:​ Por tanto, 5 + 13 + 4 + 53 = 75. El concepto de poliedro uniforme es un caso especial del concepto de , que también se aplica a las formas en el espacio de dimensiones superiores e inferiores. Geometrian, poliedro uniformea poliedro bat da, aurpegiak poligono erregularrak dituena, eta erpinak homogeneoak. Aurpegiak ez dira zertan poligono ganbilak izan: beraz, poligono uniformeetako asko izar-poliedroak dira. Simetria asko dituzten poliedroak dira. In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent. Uniform polyhedra may be regular (if also face- and edge-transitive), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular (if neither edge- nor face-transitive). The faces and vertices need not be convex, so many of the uniform polyhedra are also star polyhedra. There are two infinite classes of uniform polyhedra, together with 75 other polyhedra: Un polyèdre uniforme est un polyèdre dont les faces sont des polygones réguliers et qui est isogonal, c'est-à-dire que pour tout couple de sommets, il existe une isométrie qui applique un sommet sur l'autre. Il en découle que tous les sommets sont congruents et que le polyèdre possède un haut degré de symétrie par réflexion et rotation. La notion de polyèdre uniforme est généralisée, pour un nombre de dimensions quelconque, par celle de (en). Ils peuvent aussi être regroupés par groupe de symétrie, ce qui est fait ci-dessous. 一様多面体(いちようためんたい)とは、全ての構成面が正多角形で、かつ頂点の形状が全て合同な立体のことである。5種類の正多面体、4種類の星型正多面体、13種類の半正多面体、その他の53種類の一様多面体で総計75種類であることが、H.S.M.コクセターらによって確認され、後にによって証明された。正角柱、反角柱、ミラーの立体などもこの条件を満たすが、一様多面体には含めないことが多い。 고른 다면체는 정다각형을 면으로 가지고 점추이(그 꼭짓점에서 추이적이다. 즉, 어떤 꼭짓점에서 다른 어떤 꼭짓점으로 등거리 맵핑이 있다)인 다면체이다. 모든 꼭짓점은 합동인 것과 같다. 다면체는 (면추이와 변추이일 경우) 정다면체일 수 있고, (변추이이지만 면추이가 아닐 경우) 준정다면체이거나 (변추이도 면추이도 아닌 경우)반정다면체일 수 있다. 면과 꼭짓점은 볼록할 필요는 없어서, 많은 고른 다면체는 별 다면체이다. 다른 75개와 두 가지의 무한한 고른 다면체의 분류가 있다. * 무한한 분류 * 각기둥 * 엇각기둥 * 볼록한 예외 * 플라톤의 다면체 5개 – 볼록 정다면체 * 아르키메데스의 다면체 13개 – 볼록 준정다면체 2개와 볼록 반정다면체 11개 * 별다면체 예외 * 케플러-푸앵소 다면체 4개 – 비볼록 정다면체 * 고른 별 다면체 53개 – 준정다면체 5개와 반정다면체 48개 존 스킬링(John Skilling)이 발견한 (스킬링의 형태)를 포함해서, 모서리의 쌍이 일치하는 많은 불가능한 고른 다면체가 있다. 고른 다면체의 개념은 높은(낮은) 차원의 도형에 적용되는 의 개념의 특별한 경우이다.
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dcterms:subject
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Uniform Polyhedron
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UniformPolyhedron
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In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent. Uniform polyhedra may be regular (if also face- and edge-transitive), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular (if neither edge- nor face-transitive). The faces and vertices need not be convex, so many of the uniform polyhedra are also star polyhedra. There are two infinite classes of uniform polyhedra, together with 75 other polyhedra: * Infinite classes: * prisms, * antiprisms. * Convex exceptional: * 5 Platonic solids: regular convex polyhedra, * 13 Archimedean solids: 2 quasiregular and 11 semiregular convex polyhedra. * Star (nonconvex) exceptional: * 4 Kepler–Poinsot polyhedra: regular nonconvex polyhedra, * 53 uniform star polyhedra: 14 quasiregular and 39 semiregular. Hence 5 + 13 + 4 + 53 = 75. There are also many degenerate uniform polyhedra with pairs of edges that coincide, including one found by John Skilling called the great disnub dirhombidodecahedron (Skilling's figure). Dual polyhedra to uniform polyhedra are face-transitive (isohedral) and have regular vertex figures, and are generally classified in parallel with their dual (uniform) polyhedron. The dual of a regular polyhedron is regular, while the dual of an Archimedean solid is a Catalan solid. The concept of uniform polyhedron is a special case of the concept of uniform polytope, which also applies to shapes in higher-dimensional (or lower-dimensional) space. 一様多面体(いちようためんたい)とは、全ての構成面が正多角形で、かつ頂点の形状が全て合同な立体のことである。5種類の正多面体、4種類の星型正多面体、13種類の半正多面体、その他の53種類の一様多面体で総計75種類であることが、H.S.M.コクセターらによって確認され、後にによって証明された。正角柱、反角柱、ミラーの立体などもこの条件を満たすが、一様多面体には含めないことが多い。 Un poliedro uniforme es una figura tridimensional que tiene polígonos regulares como caras y es isogonal (es decir, presenta una isometría que permite hacer corresponder el conjunto de sus vértices entre sí mediante relaciones de simetría). De ello se deduce que todos sus vértices son congruentes.​ Los poliedros pueden ser regulares (si también son transitivos con respecto a caras y aristas), cuasirregulares (si son transitivos con respecto a sus aristas pero no con respecto a sus caras) o semirregulares (si no son transitivos de aristas ni de caras). No es necesario que la configuración de caras y de vértices sea convexa, por lo que muchos de los poliedros uniformes también son poliedros estrellados. Hay dos clases infinitas de poliedros uniformes, junto con otros 75 poliedros:​ * Clases infinitas: * Prismas * Antiprismas * Convexos excepcionales: * 5 sólidos platónicos: poliedros convexos regulares * 13 sólidos arquimedianos: 2 poliedros convexos cuasirregulares y 11 semirregulares * Estrellas (no convexos) excepcionales: * 4 sólidos de Kepler-Poinsot: poliedros regulares no convexos * 53 poliedros uniformes estrellados: 5 cuasirregulares y 48 semirregulares. Por tanto, 5 + 13 + 4 + 53 = 75. También hay muchos poliedros uniformes degenerados con pares de bordes que coinciden, incluido uno encontrado por John Skilling denominado gran dirrombidodecaedro birromo (figura de Skilling). Los poliedros conjugados de los poliedros uniformes son figuras isoedrales (es decir, isoédricas), presentan figuras de vértice regulares, y generalmente se clasifican en paralelo con su poliedro dual (uniforme). El dual de un poliedro regular es regular, mientras que el dual de un sólido de Arquímedes es un sólido de Catalan. El concepto de poliedro uniforme es un caso especial del concepto de , que también se aplica a las formas en el espacio de dimensiones superiores e inferiores. Geometrian, poliedro uniformea poliedro bat da, aurpegiak poligono erregularrak dituena, eta erpinak homogeneoak. Aurpegiak ez dira zertan poligono ganbilak izan: beraz, poligono uniformeetako asko izar-poliedroak dira. Simetria asko dituzten poliedroak dira. Un polyèdre uniforme est un polyèdre dont les faces sont des polygones réguliers et qui est isogonal, c'est-à-dire que pour tout couple de sommets, il existe une isométrie qui applique un sommet sur l'autre. Il en découle que tous les sommets sont congruents et que le polyèdre possède un haut degré de symétrie par réflexion et rotation. La notion de polyèdre uniforme est généralisée, pour un nombre de dimensions quelconque, par celle de (en). Les polyèdres uniformes peuvent être réguliers, quasi réguliers ou semi-réguliers. Les faces n'ont pas besoin d'être convexes, si bien que beaucoup de polyèdres uniformes sont étoilés. En excluant les deux ensembles infinis des prismes et antiprismes uniformes (incluant les convexes et les étoilés), il existe 75 polyèdres uniformes (ou 76 si les arêtes sont autorisées à coïncider) : * polyèdres uniformes convexes : * les 5 solides de Platon (réguliers), * les 13 solides d'Archimède (2 quasi réguliers et 11 semi-réguliers) ; * polyèdres uniformes étoilés : * les 4 réguliers : solides de Kepler-Poinsot, * les 53 non réguliers : 14 à faces convexes et 39 à faces non convexes, * 1 polyèdre avec les paires d'arêtes qui coïncident, trouvé par (en). Ils peuvent aussi être regroupés par groupe de symétrie, ce qui est fait ci-dessous. En geometria, un políedre uniforme és un políedre que admet moltes simetries, les seves cares són polígons regulars i els seus vèrtex són homogenis. Però les cares no cal que siguin per força polígons convexos: per tant, molts polígons uniformes són estelats. Vegeu també: Llista de políedres uniformes Unuforma pluredro estas unuforma hiperpluredro, 3-dimensia pluredro kiu havas regulaj plurlateroj kiel edroj kaj estas vertico-transitiva. Ĉiuj ĝiaj verticoj estas , kaj la pluredro havas altan gradon de reflekta kaj turna simetrio. Unuformaj pluredroj povas esti regula, kvazaŭregula aŭ duonregula. La edroj kaj verticoj ne nepre esta konveksaj, inter unuformaj pluredroj estas ankaŭ . Malinkluzivante la malfiniajn arojn estas 75 unuformaj pluredroj (aŭ 76 se al lateroj estas permesite koincidi). La kategorioj inkluzivas: * Malfiniaj aroj de unuformaj prismoj kaj kontraŭprismoj (inkluzivanta stelajn formojn) * 5 platonaj solidoj - regulaj konveksaj pluredroj * 4 pluredroj de Keplero-Poinsot - regulaj nekonveksaj pluredroj * 13 arĥimedaj solidoj - kvazaŭregula kaj duonregulaj konveksaj pluredroj * 14 nekonveksaj pluredroj kun konveksaj edroj * 39 nekonveksaj pluredroj kun nekonveksaj edroj * 1 pluredro trovita de ĉe kiu paroj de lateroj koincidas. Ili povas ankaŭ esti grupita per ilia geometria simetria grupo, kio estas farita pli sube. 고른 다면체는 정다각형을 면으로 가지고 점추이(그 꼭짓점에서 추이적이다. 즉, 어떤 꼭짓점에서 다른 어떤 꼭짓점으로 등거리 맵핑이 있다)인 다면체이다. 모든 꼭짓점은 합동인 것과 같다. 다면체는 (면추이와 변추이일 경우) 정다면체일 수 있고, (변추이이지만 면추이가 아닐 경우) 준정다면체이거나 (변추이도 면추이도 아닌 경우)반정다면체일 수 있다. 면과 꼭짓점은 볼록할 필요는 없어서, 많은 고른 다면체는 별 다면체이다. 다른 75개와 두 가지의 무한한 고른 다면체의 분류가 있다. * 무한한 분류 * 각기둥 * 엇각기둥 * 볼록한 예외 * 플라톤의 다면체 5개 – 볼록 정다면체 * 아르키메데스의 다면체 13개 – 볼록 준정다면체 2개와 볼록 반정다면체 11개 * 별다면체 예외 * 케플러-푸앵소 다면체 4개 – 비볼록 정다면체 * 고른 별 다면체 53개 – 준정다면체 5개와 반정다면체 48개 존 스킬링(John Skilling)이 발견한 (스킬링의 형태)를 포함해서, 모서리의 쌍이 일치하는 많은 불가능한 고른 다면체가 있다. 고른 다면체의 쌍대다면체는 면추이이고 꼭짓점 도형이 정다각형이고, 일반적으로 (고른) 쌍대다면체와 나란하게 분류된다. 정다면체의 쌍대는 정다면체이고, 아르키메데스의 다면체의 쌍대는 카탈랑의 다면체이다. 고른 다면체의 개념은 높은(낮은) 차원의 도형에 적용되는 의 개념의 특별한 경우이다. 在幾何學中,均勻多面體是指由正多邊形面構成且具有頂點可遞特性的多面體,點可遞代表該幾何結構中的任2個頂點其中一個頂點可以透過平移、旋轉與鏡射的過程映射到另一個頂點,換句話說這個幾何結構的頂角是全等的,所以該多面體具有具有高度鏡射和旋轉對稱。 均勻多面體可能是正多面體(同時具備面可遞、邊可遞)、擬正多面體(若邊可遞,則面不可遞)或半正多面體(邊未必可遞面也未必可遞)。由於面和頂角不一定要是凸的,所以很多均勻多面體的也是星狀多面體。 不包括無限集合,有75個均勻多面體(如果允許邊緣重合則有76種)。 * 凸多面體 * 5種凸正多面體 * 13種阿基米德立體——兩種擬正多面體和11種半正多面體 * 星狀多面體 * 4種克卜勒-龐索立體——正非凸多面體 * 53種均勻星形多面體——5種擬正多面體和48種半正多面體 * 1種由約翰·斯基林發現與對邊重合的星狀多面體,稱為大二重扭稜二重斜方十二面體或斯基林圖形(Skilling's figure)。 In geometria, un poliedro uniforme è un poliedro che ammette molte simmetrie, le cui facce sono poligoni regolari e i cui vertici sono omogenei. Le facce non devono però essere necessariamente convesse: molti poliedri uniformi sono quindi stellati.
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