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quarter cubic honeycomb : ウィキペディア英語版
quarter cubic honeycomb

|-
|bgcolor=#e7dcc3|Coxeter-Dynkin diagram|| = =
|-
|bgcolor=#e7dcc3|Cell types||
(3.6.6)
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|bgcolor=#e7dcc3|Face types||,
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|bgcolor=#e7dcc3|Vertex figure||80px
(isosceles triangular antiprism)
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|bgcolor=#e7dcc3|Space group||Fdm (227)
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|bgcolor=#e7dcc3|Coxeter group||
The quarter cubic honeycomb, quarter cubic cellulation or bitruncated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of tetrahedra and truncated tetrahedra in a ratio of 1:1. It is called "quarter-cubic" because its symmetry unit – the minimal block from which the pattern is developed by reflections – consists of four such units of the cubic honeycomb.
It is vertex-transitive with 6 truncated tetrahedra and 2 tetrahedra around each vertex.
It is one of the 28 convex uniform honeycombs.
The faces of this honeycomb's cells form four families of parallel planes, each with a 3.6.3.6 tiling.
Its vertex figure is an isosceles antiprism: two equilateral triangles joined by six isosceles triangles.
John Horton Conway calls this honeycomb a truncated tetrahedrille, and its dual oblate cubille.
The vertices and edges represent a Kagome lattice in three dimensions.
== Construction==

The quarter cubic honeycomb can be constructed in slab layers of truncated tetrahedra and tetrahedral cells, seen as two trihexagonal tilings. Two tetrahedra are stacked by a vertex and a central inversion. In each trihexagonal tiling, half of the triangles belong to tetrahedra, and half belong to truncated tetrahedra. These slab layers must be stacked with tetrahedra triangles to truncated tetrahedral triangles to construct the uniform ''quarter cubic honeycomb''. Slab layers of hexagonal prisms and triangular prisms can be alternated for ''elongated'' honeycombs, but these are also not uniform.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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