Acronym dis
Name disnubihedron,
compound of 12 tet
 
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Circumradius sqrt(3/8) = 0.612372
Inradius 1/sqrt(24) = 0.204124
Vertex figure [33]
Dihedral angles
(at margins)
  • between {3} and {3}:   arccos(1/3) = 70.528779°
Confer
related compounds:
so   sis   risdoh  
External
links
hedrondude   wikipedia  

This compound has rotational freedom. Starting at φ = 0° with a completely coincident overlay of 6 stella octangula (so), rotating 2 stella octangula each, thought of each as a pair of 2-fold antiprisms, around their common axis in opposite directions.

Either the tet can be considered separately (type A); or they are considered as so (type B). Further this is a compound of 2 sis (both tetrahedral subsets are used - type C). Therefore, for φ = 45° this gives a double cover of snu.

This compound can be vertex-inscribed (with full rotational freedom) into risdoh in the same way as each individual so will be inscribed into each of those cubes.


Incidence matrix

(Type A)

 48 |  1  2 |  3 ||  1
----+-------+----++---
  2 | 24  * |  1 ||  1
  2 |  * 48 |  2 ||  1
----+-------+----++---
  3 |  1  2 | 48 ||  1
----+-------+----++---
 4 |  2  4 |  4 || 12

(Type B)

 48 |  1  2 |  3 || 1
----+-------+----++--
  2 | 24  * |  1 || 1
  2 |  * 48 |  2 || 1
----+-------+----++--
  3 |  1  2 | 48 || 1
----+-------+----++--
 8 |  4  8 |  8 || 6

(Type C)

  48 |  1  2 |  3 || 1
-----+-------+----++--
   2 | 24  * |  1 || 1
   2 |  * 48 |  2 || 1
-----+-------+----++--
   3 |  1  2 | 48 || 1
-----+-------+----++--
 24 | 12 24 | 24 || 2

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