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In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus simus) and snub dodecahedron (dodecaedron simum). In general, snubs have chiral symmetry with two forms: with clockwise or counterclockwise orientation. By Kepler's names, a snub can be seen as an expansion of a regular polyhedron: moving the faces apart, twisting them about their centers, adding new polygons centered on the original vertices, and adding pairs of triangles fitting between the original edges.

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  • Achatado (geometría) (es)
  • Snub (geometry) (en)
  • Операция «Snub» (ru)
  • 扭稜 (zh)
rdfs:comment
  • 在幾何學中,扭稜是一種多面體變換。該術語起源於开普勒對阿基米德立體的命名,分別為扭棱立方体(英語:snub cube、拉丁語:cubus simus)和扭棱十二面体(英語:snub dodecahedron、拉丁語:dodecaedron simum)。一般而言,多面體經扭稜變換後可以形成兩種互為手性鏡像的形式,分別為順時針方向的扭稜和逆時針方向的扭稜。以开普勒的命名對應的扭稜變換可以看做是正多面體的擴張,也就是將正多面體的面向外分開,並圍繞著中心扭曲(不改變面的形狀),然後加入以每個原始立體頂點為中心的正方形,並在每個原始立體之邊的位置上加入成對的三角形來構成。 考克斯特對扭稜進行了推廣,推廣成能用於更廣泛的均勻多面體,其定義略有不同。 (zh)
  • En geometría, el achatado es una operación aplicada a un poliedro que permite obtener a partir de él un . El término utilizado para denominar a esta operación en inglés (snub), tiene su origen en los nombres dados a dos sólidos arquimedianos (el cubo romo y el dodecaedro romo) por Johannes Kepler, quien los llamó cubus simus y dodecaedron simum.​ En general, los poliedros romos presentan dos formas con simetría quiral: con orientación horaria o antihoraria. Según los nombres de Kepler, un poliedro romo puede verse como una de un poliedro regular mediante el procedimiento siguiente: separando las caras, girándolas alrededor de sus centros, agregando nuevos polígonos centrados en los vértices originales y agregando pares de triángulos que se ajustan entre las aristas originales. (es)
  • In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus simus) and snub dodecahedron (dodecaedron simum). In general, snubs have chiral symmetry with two forms: with clockwise or counterclockwise orientation. By Kepler's names, a snub can be seen as an expansion of a regular polyhedron: moving the faces apart, twisting them about their centers, adding new polygons centered on the original vertices, and adding pairs of triangles fitting between the original edges. (en)
  • Операция snub или отсечение вершин — это операция, применяемая к многогранникам. Термин появился из названий, данных Кеплером двум архимедовым телам — плосконосый куб (cubus simus) и плосконосый додекаэдр (dodecaedron simum). В общем случае плосконосые формы имеют хиральную симметрию двух видов, с ориентацией по часовой стрелке и против часовой стрелки. Согласно названиям Кеплера, отсечение вершин можно рассматривать как растяжение правильного многогранника, когда исходные грани отодвигаются от центра и поворачиваются относительно центров, вместо исходных вершин добавляются многоугольники с центрами в этих вершинах, а пары треугольников заполняют пространство между исходными рёбрами. (ru)
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