Acronym | risdoh |
Name |
rhombisnub dishexahedron, compound of 6 cube, Skilling's compound |
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Circumradius | sqrt(3)/2 = 0.866025 |
Inradius | 1/2 |
Vertex figure | [43] |
Coordinates |
(c+s, c-s, 1)/2 all permutations, all changes of sign where c = cos(φ), s = sin(φ) |
Dihedral angles
(at margins) |
|
Confer | rah sis dis |
External links |
This compound has rotational freedom. Starting at φ = 0° with a completely coincident overlay of 6 cubes, rotating 2 cubes each, thought of as 4-fold prisms, around their common axis in opposite directions, and thereby passing at φ = 45° at a double cover of rah.
Bases of those 4-fold prisms pairwise fall into coincident face planes. So either they can be considered separately (type A); or they are considered as (rotated) 2-square-compounds (type B).
This compound can be vertex-superimposed (with full rotational freedom) to dis in the same way as each individual cube will be vertex-superimposed to each of those so. Furthermore, half its vertices can likewise be vertex-superimposed (with full rotational freedom) to sis in the same way as each individual cube will be related to the inscribed tet.
(Type A) 48 | 2 1 | 2 1 || 1 ----+-------+-------++-- 2 | 48 * | 1 1 || 1 2 | * 24 | 2 0 || 1 ----+-------+-------++-- 4 | 2 2 | 24 * || 1 4 | 4 0 | * 12 || 1 ----+-------+-------++-- ♦ 8 | 8 4 | 4 2 || 6
(Type B) 48 | 2 1 | 2 1 || 1 ----+-------+------++-- 2 | 48 * | 1 1 || 1 2 | * 24 | 2 0 || 1 ----+-------+------++-- 4 | 2 2 | 24 * || 1 8 | 8 0 | * 6 || 2 ----+-------+------++-- ♦ 8 | 8 4 | 4 2 || 6
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