Acronym dissit
Name disnub tetrahedron,
compound of 4 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:
doso   sno   se  
External
links
hedrondude   wikipedia  

This compound has rotational freedom. Starting at φ = 0° with a completely coincident overlay of 4 octahedra, rotating 1 octahedron each, thought of as 3-fold antiprisms, around a tetrahedral subset of trigonal axes, and thereby passing at φ = 60° at sno.

This is the hemi-version of doso.

For an intermediate state of φ the lateral triangles become coplanar, and thus can be considered as (rotated) 2-triangle-compounds. That special case is called hidsit (hexagrammattic disnub tetrahedron). By coincidence, hidsit is nothing but se with 1 oct removed. (Jonathan further uses idsit (inner ...) for smaller values of φ, resp. odsit (outer ...) for larger values.)


Incidence matrix

 24 |  2  2 |  3 1 || 1
----+-------+------++--
  2 | 24  * |  1 1 || 1
  2 |  * 24 |  2 0 || 1
----+-------+------++--
  3 |  1  2 | 24 * || 1
  3 |  3  0 |  * 8 || 1
----+-------+------++--
 6 |  6  6 |  6 2 || 4

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