Cuboctahedron (original) (raw)
En geometria, el cubooctaedre o cubooctàedre és un dels tretze políedres arquimedians. S'obté truncant els vuit vèrtexs del cub, o bé els sis vèrtexs de l'octàedre regular. Té 14 cares, 6 de les quals són quadrades i 8 triangulars, cada una de les seves 24 arestes separa una cara quadrada d'una triangular i a cadascun dels seus 12 vèrtexs hi concorren dues cares quadrades i dues triangulars.
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| dbo:abstract | En geometria, el cubooctaedre o cubooctàedre és un dels tretze políedres arquimedians. S'obté truncant els vuit vèrtexs del cub, o bé els sis vèrtexs de l'octàedre regular. Té 14 cares, 6 de les quals són quadrades i 8 triangulars, cada una de les seves 24 arestes separa una cara quadrada d'una triangular i a cadascun dels seus 12 vèrtexs hi concorren dues cares quadrades i dues triangulars. (ca) Das Kuboktaeder (auch Kubooktaeder oder Kubo-Oktaeder) ist ein Polyeder (Vielflächner) mit 14 Seiten (6 Quadrate und 8 regelmäßige Dreiecke), 12 gleichartigen Ecken und 24 gleich langen Kanten. Aufgrund seiner Regelmäßigkeit zählt das Kuboktaeder zu den 13 archimedischen Körpern. Neben dem Ikosidodekaeder ist es der einzige konvexe quasireguläre Körper. Der Umkugelradius (Abstand der Ecken zum Mittelpunkt) ist wie beim Antikuboktaeder gleich der Kantenlänge. Sein Dualkörper ist das Rhombendodekaeder. (de) Στη Στερεομετρία, το κυβοκτάεδρο είναι ένα κυρτό ημικανονικό πολύεδρο, που ανήκει στα στερεά του Αρχιμήδη. Διαθέτει 14 έδρες: 8 ισόπλευρα τρίγωνα και 6 τετράγωνα. Έχει 12 κορυφές και 24 ακμές. Η του είναι (3.4.3.4), δηλαδή σε κάθε κορυφή του ενώνονται εναλλάξ δύο τρίγωνα και δύο τετράγωνα. Όλες οι ακμές σχηματίζουν έναν σκελετό τεσσάρων κανονικών εξαγώνων, που τέμνονται ανά δύο στις κορυφές του πολυέδρου. (el) Kubokedro estas pluredro kun ok triangulaj edroj kaj ses kvadrataj edroj. Kubokedro havas 12 identajn verticojn, kun du trianguloj kaj du kvadratoj kuniĝantaj je ĉiu, kaj 24 identajn laterojn, kiuj ĉiu kunigas triangulon kaj kvadraton. Ĝi estas kvazaŭregula pluredro, arĥimeda solido, vertico-transitiva kaj latero-transitiva. (eo) A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral. Its dual polyhedron is the rhombic dodecahedron. The cuboctahedron was probably known to Plato: Heron's Definitiones quotes Archimedes as saying that Plato knew of a solid made of 8 triangles and 6 squares. (en) Geometrian, Kuboktaedroa Arkimedesen solidoetako bat da, 14 aurpegi (8 hiruki aldeberdin eta 6 karratu), 24 ertz eta 12 erpin dituena. (eu) El cuboctaedro es un sólido de Arquímedes que se obtiene truncando cada vértice de un cubo con lo que resultan 14 caras: 6 del cubo, que continúan cuadradas y 8 nuevas -en forma de triángulos equiláteros- que resultan del truncamiento de los vértices; el cuboctaedro es un cubo que se trunca hasta el punto medio de la arista; en este sentido tiene mucha relación con el cubo truncado y el octaedro. El área de un cuboctaedro con una arista de tamaño a es y su volumen: (es) Un cuboctaèdre est un polyèdre à 14 faces régulières, dont huit sont des triangles équilatéraux et six sont des carrés. Il comporte : * 12 sommets identiques, chacun joignant deux triangles et deux carrés opposés deux à deux ; * 24 arêtes identiques, chacune commune à un triangle et à un carré. Il s'agit donc d'un polyèdre quasi-régulier, c’est-à-dire un solide d'Archimède (uniformité des sommets) avec en plus, une uniformité des arêtes. On obtient ce polyèdre en tronquant un solide de Platon de douze arêtes (cube ou octaèdre régulier) à chaque sommet, par une section qui passe par les milieux de toutes les arêtes issues du sommet tronqué. Ses vingt-quatre arêtes égales sont les côtés de quatre hexagones réguliers concentriques : quatre sections équatoriales du solide tronqué ou du solide initial (cube ou octaèdre régulier). Il a été baptisé par Kepler. Les côtés des six hexagones réguliers concentriques sont égaux aux rayons de leurs cercles circonscrits, six grands cercles de la sphère circonscrite au cuboctaèdre. La distance d'un sommet au centre du cuboctaèdre est donc égale à la longueur d'un côté. Son polyèdre dual est le dodécaèdre rhombique. Ce polyèdre est utilisé par le Rainbow Cube, une variante du Rubik's Cube. (fr) 立方八面体 (りっぽうはちめんたい、英: cuboctahedron)またはベクトル平衡体 (-へいこうたい、英: vector equilibrium)、異相双三角台塔（いそうそうさんかくだいとう、英: triangular gyrobicupola）とは、半正多面体、準正多面体の一種で、正六面体または正八面体の各頂点を辺の中心まで切り落とした立体である。正四面体の辺を削ったような形や、2つの正三角台塔を底面同士で60°ずらして張り付けた形にもなっている。 (ja) 육팔면체는 정육면체와 정육면체의 쌍대다면체인 정팔면체의 중간이다. 면의 수는 14개, 모서리의 수는 24개, 꼭짓점의 수는 12개이다. 또 육팔면체는 정육면체의 꼭짓점이나 정팔면체의 꼭짓점을 모서리의 1/2 정도 깎아서도 만들 수 있다. 이것은 비틀어 붙인 삼각지붕으로 볼 수 있다. = 비틀어 붙인 삼각지붕 (ko) In geometria solida, il cubottaedro è uno dei tredici poliedri archimedei, ottenuto troncando le otto cuspidi del cubo, oppure le sei cuspidi dell'ottaedro regolare. Ha 14 facce, di cui 6 quadrate e 8 triangolari, ognuno dei suoi 24 spigoli separa una faccia quadrata da una triangolare e in ciascuno dei suoi 12 vertici concorrono due facce quadrate e due triangolari. (it) Een kuboctaëder of halfregelmatig veertienvlak is een archimedisch lichaam, dus ook een halfregelmatig veelvlak. Het is een van de twee convexe veelvlakken, die niet zijvlaktransitief zijn, maar wel ribbetransitief. Het andere is de icosidodecaëder. Het heeft 14 zijvlakken, waarvan 8 driehoeken en 6 vierkanten, 12 hoekpunten en 24 ribben. Het is de coördinatiepolyeder in de kristalstructuur van indium. Een kuboctaëder ontstaat door de acht hoekpunten van een kubus af te knotten, net zoals bij de afgeknotte kubus, maar dan zo dat van elk zijvlak slechts een gedraaid vierkant overblijft in plaats van een achthoek, of door de zes hoekpunten van een regelmatig achtvlak af te knotten. Het is daarmee een figuur tussen de kubus en het regelmatige achtvlak in. In ieder hoekpunt van een kuboactaëder snijden twee regelmatige zeshoeken elkaar, die de kuboactaëder omschrijven. Dat zijn vier regelmatige zeshoeken. De oppervlakte A en inhoud V van een kuboctaëder waarbij a de lengte van een ribbe is, worden gegeven door: De kuboctaëder uitgevouwen: Er zijn verschillende manieren, waarop kuboctaëders zonder ruimteverlies zijn te stapelen, samen met * regelmatige achtvlakken, * kubussen en romboëdrische kuboctaëders en * afgeknotte octaëders en afgeknotte tetraëders. (nl) Кубоокта́эдр или кубокта́эдр — полуправильный многогранник (архимедово тело) с 14 гранями, составленный из 8 правильных треугольников и 6 квадратов. В каждой из его 12 одинаковых вершин сходятся две квадратных грани и две треугольных. Телесный угол при вершине равен Кубооктаэдр имеет 24 ребра равной длины. Двугранный угол при любом ребре одинаков и равен Кубооктаэдр можно получить из куба, «срезав» с него 8 правильных треугольных пирамид; либо из октаэдра, «срезав» с него 6 квадратных пирамид; либо как пересечение имеющих общий центр куба и октаэдра. (ru) Um cuboctaedro é um poliedro com 8 faces triangulares e 6 faces quadrangulares. O cuboctaedro pode não ser realizado, considerando os pontos médios das arestas e unindo esses pontos por uma aresta, se eles pertencerem a arestas adjacentes de uma face do cubo; mas também pode ser obtido a partir do octaedro, o dual do cubo, considerado como arestas os segmentos que unem os pontos médios dos lados das faces triangulares do octaedro. (pt) Sześcio-ośmiościan (kuboktaedr) – wielościan, który posiada 12 wierzchołków, 24 krawędzi, 14 ścian (8 trójkątów równobocznych, 6 kwadratów). Jest bryłą archimedesową dualną z dwunastościanem rombowym. (pl) Kuboktaeder är en arkimedisk kropp som inom geometri är en konvex tredimensionell geometrisk kropp (polyeder). En kuboktaeder består av 14 sidor uppdelat på 8 liksidiga trianglar och 6 kvadrater. Ytorna bildar 24 kanter och 12 hörn. (sv) 在幾何學中，截半立方體是一種十四面體，由八個三角形與六個正方形組成，具有14個面、12個頂點以及24條邊。是一種阿基米德立體，屬於半正多面體和擬正多面體。其對偶多面體為菱形十二面體。 (zh) Кубооктаедр — напівправильний многогранник, що складається із 14 граней (8 із яких є правильним трикутником і 6, відповідно, квадратом). В кубооктаедрі 12 однакових вершин, в яких сходяться два трикутники і два квадрати, а також 24 однакових ребра, кожне з яких розділяє між собою трикутник і квадрат. Двоїстий до кубооктаедра многогранник — ромбододекаедр. (uk) |
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| rdfs:comment | En geometria, el cubooctaedre o cubooctàedre és un dels tretze políedres arquimedians. S'obté truncant els vuit vèrtexs del cub, o bé els sis vèrtexs de l'octàedre regular. Té 14 cares, 6 de les quals són quadrades i 8 triangulars, cada una de les seves 24 arestes separa una cara quadrada d'una triangular i a cadascun dels seus 12 vèrtexs hi concorren dues cares quadrades i dues triangulars. (ca) Das Kuboktaeder (auch Kubooktaeder oder Kubo-Oktaeder) ist ein Polyeder (Vielflächner) mit 14 Seiten (6 Quadrate und 8 regelmäßige Dreiecke), 12 gleichartigen Ecken und 24 gleich langen Kanten. Aufgrund seiner Regelmäßigkeit zählt das Kuboktaeder zu den 13 archimedischen Körpern. Neben dem Ikosidodekaeder ist es der einzige konvexe quasireguläre Körper. Der Umkugelradius (Abstand der Ecken zum Mittelpunkt) ist wie beim Antikuboktaeder gleich der Kantenlänge. Sein Dualkörper ist das Rhombendodekaeder. (de) Στη Στερεομετρία, το κυβοκτάεδρο είναι ένα κυρτό ημικανονικό πολύεδρο, που ανήκει στα στερεά του Αρχιμήδη. Διαθέτει 14 έδρες: 8 ισόπλευρα τρίγωνα και 6 τετράγωνα. Έχει 12 κορυφές και 24 ακμές. Η του είναι (3.4.3.4), δηλαδή σε κάθε κορυφή του ενώνονται εναλλάξ δύο τρίγωνα και δύο τετράγωνα. Όλες οι ακμές σχηματίζουν έναν σκελετό τεσσάρων κανονικών εξαγώνων, που τέμνονται ανά δύο στις κορυφές του πολυέδρου. (el) Kubokedro estas pluredro kun ok triangulaj edroj kaj ses kvadrataj edroj. Kubokedro havas 12 identajn verticojn, kun du trianguloj kaj du kvadratoj kuniĝantaj je ĉiu, kaj 24 identajn laterojn, kiuj ĉiu kunigas triangulon kaj kvadraton. Ĝi estas kvazaŭregula pluredro, arĥimeda solido, vertico-transitiva kaj latero-transitiva. (eo) A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral. Its dual polyhedron is the rhombic dodecahedron. The cuboctahedron was probably known to Plato: Heron's Definitiones quotes Archimedes as saying that Plato knew of a solid made of 8 triangles and 6 squares. (en) Geometrian, Kuboktaedroa Arkimedesen solidoetako bat da, 14 aurpegi (8 hiruki aldeberdin eta 6 karratu), 24 ertz eta 12 erpin dituena. (eu) El cuboctaedro es un sólido de Arquímedes que se obtiene truncando cada vértice de un cubo con lo que resultan 14 caras: 6 del cubo, que continúan cuadradas y 8 nuevas -en forma de triángulos equiláteros- que resultan del truncamiento de los vértices; el cuboctaedro es un cubo que se trunca hasta el punto medio de la arista; en este sentido tiene mucha relación con el cubo truncado y el octaedro. El área de un cuboctaedro con una arista de tamaño a es y su volumen: (es) 立方八面体 (りっぽうはちめんたい、英: cuboctahedron)またはベクトル平衡体 (-へいこうたい、英: vector equilibrium)、異相双三角台塔（いそうそうさんかくだいとう、英: triangular gyrobicupola）とは、半正多面体、準正多面体の一種で、正六面体または正八面体の各頂点を辺の中心まで切り落とした立体である。正四面体の辺を削ったような形や、2つの正三角台塔を底面同士で60°ずらして張り付けた形にもなっている。 (ja) 육팔면체는 정육면체와 정육면체의 쌍대다면체인 정팔면체의 중간이다. 면의 수는 14개, 모서리의 수는 24개, 꼭짓점의 수는 12개이다. 또 육팔면체는 정육면체의 꼭짓점이나 정팔면체의 꼭짓점을 모서리의 1/2 정도 깎아서도 만들 수 있다. 이것은 비틀어 붙인 삼각지붕으로 볼 수 있다. = 비틀어 붙인 삼각지붕 (ko) In geometria solida, il cubottaedro è uno dei tredici poliedri archimedei, ottenuto troncando le otto cuspidi del cubo, oppure le sei cuspidi dell'ottaedro regolare. Ha 14 facce, di cui 6 quadrate e 8 triangolari, ognuno dei suoi 24 spigoli separa una faccia quadrata da una triangolare e in ciascuno dei suoi 12 vertici concorrono due facce quadrate e due triangolari. (it) Кубоокта́эдр или кубокта́эдр — полуправильный многогранник (архимедово тело) с 14 гранями, составленный из 8 правильных треугольников и 6 квадратов. В каждой из его 12 одинаковых вершин сходятся две квадратных грани и две треугольных. Телесный угол при вершине равен Кубооктаэдр имеет 24 ребра равной длины. Двугранный угол при любом ребре одинаков и равен Кубооктаэдр можно получить из куба, «срезав» с него 8 правильных треугольных пирамид; либо из октаэдра, «срезав» с него 6 квадратных пирамид; либо как пересечение имеющих общий центр куба и октаэдра. (ru) Um cuboctaedro é um poliedro com 8 faces triangulares e 6 faces quadrangulares. O cuboctaedro pode não ser realizado, considerando os pontos médios das arestas e unindo esses pontos por uma aresta, se eles pertencerem a arestas adjacentes de uma face do cubo; mas também pode ser obtido a partir do octaedro, o dual do cubo, considerado como arestas os segmentos que unem os pontos médios dos lados das faces triangulares do octaedro. (pt) Sześcio-ośmiościan (kuboktaedr) – wielościan, który posiada 12 wierzchołków, 24 krawędzi, 14 ścian (8 trójkątów równobocznych, 6 kwadratów). Jest bryłą archimedesową dualną z dwunastościanem rombowym. (pl) Kuboktaeder är en arkimedisk kropp som inom geometri är en konvex tredimensionell geometrisk kropp (polyeder). En kuboktaeder består av 14 sidor uppdelat på 8 liksidiga trianglar och 6 kvadrater. Ytorna bildar 24 kanter och 12 hörn. (sv) 在幾何學中，截半立方體是一種十四面體，由八個三角形與六個正方形組成，具有14個面、12個頂點以及24條邊。是一種阿基米德立體，屬於半正多面體和擬正多面體。其對偶多面體為菱形十二面體。 (zh) Кубооктаедр — напівправильний многогранник, що складається із 14 граней (8 із яких є правильним трикутником і 6, відповідно, квадратом). В кубооктаедрі 12 однакових вершин, в яких сходяться два трикутники і два квадрати, а також 24 однакових ребра, кожне з яких розділяє між собою трикутник і квадрат. Двоїстий до кубооктаедра многогранник — ромбододекаедр. (uk) Un cuboctaèdre est un polyèdre à 14 faces régulières, dont huit sont des triangles équilatéraux et six sont des carrés. Il comporte : * 12 sommets identiques, chacun joignant deux triangles et deux carrés opposés deux à deux ; * 24 arêtes identiques, chacune commune à un triangle et à un carré. Il a été baptisé par Kepler. Les côtés des six hexagones réguliers concentriques sont égaux aux rayons de leurs cercles circonscrits, six grands cercles de la sphère circonscrite au cuboctaèdre. La distance d'un sommet au centre du cuboctaèdre est donc égale à la longueur d'un côté. (fr) Een kuboctaëder of halfregelmatig veertienvlak is een archimedisch lichaam, dus ook een halfregelmatig veelvlak. Het is een van de twee convexe veelvlakken, die niet zijvlaktransitief zijn, maar wel ribbetransitief. Het andere is de icosidodecaëder. Het heeft 14 zijvlakken, waarvan 8 driehoeken en 6 vierkanten, 12 hoekpunten en 24 ribben. Het is de coördinatiepolyeder in de kristalstructuur van indium. De oppervlakte A en inhoud V van een kuboctaëder waarbij a de lengte van een ribbe is, worden gegeven door: De kuboctaëder uitgevouwen: (nl) |
| rdfs:label | Cuboctahedron (en) Cubooctàedre (ca) Kuboktaeder (de) Κυβοκτάεδρο (el) Kubokedro (eo) Cuboctaedro (es) Kuboktaedro (eu) Cuboctaèdre (fr) Cubottaedro (it) 立方八面体 (ja) 육팔면체 (ko) Sześcio-ośmiościan (pl) Kuboctaëder (nl) Кубооктаэдр (ru) Cuboctaedro (pt) 截半立方體 (zh) Kuboktaeder (sv) Кубооктаедр (uk) |
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