Acronym doso
Name disnub octahedron,
compound of 8 oct
 
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Circumradius 1/sqrt(2) = 0.707107
Inradius 1/sqrt(6) = 0.408248
Vertex figure [34]
Dihedral angles
(at margins)
  • between {3} and {3}:   arccos(-1/3) = 109.471221°
Confer
related compounds:
dissit   sno  
External
links
hedrondude   wikipedia  

This compound has rotational freedom. Starting at φ = 0° with a completely coincident overlay of 8 octahedra, rotating 2 octahedra each, thought of as 3-fold antiprisms, around their common axis in opposite directions, and thereby passing at φ = 60° at a double cover of sno.

Bases of those 3-fold antiprisms pairwise fall into coincident face planes. So either they can be considered separately (type A); or they are considered as (rotated) 2-triangle-compounds (type B).

This also is a compound of 2 dissit (both tetrahedral subsets are used - type C).

For an intermediate state of φ the lateral triangles too become coplanar, and thus can be considered as (rotated) 2-triangle-compounds. That special case is called hidso (hexagrammattic disnub octahedron). (Jonathan further uses idso (inner ...) for smaller values of φ, resp. odso (outer ...) for greater values.)


Incidence matrix

(Type A)

 48 |  2  2 |  3  1 || 1
----+-------+-------++--
  2 | 48  * |  1  1 || 1
  2 |  * 48 |  2  0 || 1
----+-------+-------++--
  3 |  1  2 | 48  * || 1
  3 |  3  0 |  * 16 || 1
----+-------+-------++--
 6 |  6  6 |  6  2 || 8

(Type B)

 48 |  2  2 |  3 1 || 1
----+-------+------++--
  2 | 48  * |  1 1 || 1
  2 |  * 48 |  2 0 || 1
----+-------+------++--
  3 |  1  2 | 48 * || 1
  6 |  6  0 |  * 8 || 2
----+-------+------++--
 6 |  6  6 |  6 2 || 8

(Type C)

  48 |  2  2 |  3  1 || 1
-----+-------+-------++--
   2 | 48  * |  1  1 || 1
   2 |  * 48 |  2  0 || 1
-----+-------+-------++--
   3 |  1  2 | 48  * || 1
   3 |  3  0 |  * 16 || 1
-----+-------+-------++--
 24 | 24 24 | 24  8 || 2

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