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In geometry, the elongated dodecahedron, extended rhombic dodecahedron, rhombo-hexagonal dodecahedron or hexarhombic dodecahedron is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi. It can be seen as constructed from a rhombic dodecahedron elongated by a square prism. Along with the rhombic dodecahedron, it is a space-filling polyhedron, one of the five types of parallelohedron identified by Evgraf Fedorov that tile space face-to-face by translations.

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  • Elongated dodecahedron (en)
  • Verlängertes Rhombendodekaeder (de)
  • Rombo-seslatera dekduedro (eo)
  • 長菱形十二面体 (ja)
  • 菱形六角化十二面體 (zh)
rdfs:comment
  • In geometry, the elongated dodecahedron, extended rhombic dodecahedron, rhombo-hexagonal dodecahedron or hexarhombic dodecahedron is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi. It can be seen as constructed from a rhombic dodecahedron elongated by a square prism. Along with the rhombic dodecahedron, it is a space-filling polyhedron, one of the five types of parallelohedron identified by Evgraf Fedorov that tile space face-to-face by translations. (en)
  • 長菱形十二面体 (ちょうりょうけいじゅうにめんたい、elongated rhombic dodecahedron)とは、5種類ある平行多面体(平行移動のみで空間を隙間なく充填できる立体の類型)の一種で、菱形十二面体を長軸方向に引き伸ばしたような形をしている。 * 構成面:菱形 8枚、平行六辺形 4枚 * 辺:28 * 頂点:18 14種類ある3次元結晶格子のうちの、体心正方格子のボロノイ図形にあたる。 いいかえると、断面正方形の四角柱をピラミッドのように積み上げたときに、四角柱の重心に格子点があるとみなして描いたボロノイ図形が長菱形十二面体である。 (ja)
  • 在幾何學中,菱形六角化十二面體(rhombo-hexagonal dodecahedron或hexarhombic dodecahedron)是一個平行多面體,由8個菱形4個等邊六邊形組成,也稱為拉長的十二面體(elongated dodecahedron)或擴張的菱形十二面體,因為它可以透過將菱形十二面體的其中4個菱形面擴大(或拉長)成六邊形來構造。 (zh)
  • La rombo-seslatera dekduedro estas konveksa pluredro kun 8 rombaj kaj 4 egallateraj seslateraj edroj. Ĝi estas nomata ankaŭ kiel plilongigita dekduedro aŭ etendita romba dekduedro ĉar ĝi estas rilatanta al la romba dekduedro per elvolvado de kvar rombaj edroj de la romba dekduedro en seslaterojn. Ĝi pro tio havas kelkajn la samajn propraĵoj kiel la romba dekduedro: (eo)
  • Das Verlängerte Rhombendodekaeder ist ein konvexes Dodekaeder mit acht Rhomben und vier Hexagonen als Seiten, 18 Ecken und 28 Kanten. Es ist eines von fünf sogenannten Paralleloedern, das heißt konvexen Polyedern, die durch Translation den Raum parkettieren. Sie wurden von Jewgraf Stepanowitsch Fjodorow 1885 gefunden. Die anderen vier sind Parallelepiped, hexagonales Prisma, Rhombendodekaeder und Oktaederstumpf. Ein Bild des verlängerten Rhombendodekaeders findet sich eingemeißelt auf dem Grabstein von Arthur Schoenflies, einem der frühen Klassifizierer der Raumgruppen neben Fjodorow. (de)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/Rhombo-hexagonal_dodecahedron.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Rhombo-hexagonal_dodecahedron_tessellation.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Contracted_truncated_octahedron.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Contracted_truncated_octahedron_honeycomb.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Contracted_truncated_octahedron_net.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Elongated_dodecahedron_concave.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Elongated_dodecahedron_concave_honeycomb.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Elongated_dodecahedron_concave_net.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Elongated_dodecahedron_flat.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Elongated_dodecahedron_flat_honeycomb.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Elongated_dodecahedron_flat_net.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Elongated_dodecahedron_net.png
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  • Elongated_dodecahedron_net.png (en)
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symmetry
  • Dihedral order 16 (en)
title
  • Space-filling polyhedron (en)
  • Elongated dodecahedron (en)
type
urlname
  • Space-FillingPolyhedron (en)
  • ElongatedDodecahedron (en)
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