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)
  • between {4} and {4}:   90°
Confer rah   sis   dis  
External
links
hedrondude   wikipedia   mathworld

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.


Incidence matrix

(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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