Acronym desided
Name disnub icosidodecadodecahedron,
compound of 2 sided
 
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Circumradius sqrt[(2ρ-1)/(ρ-1)] = 1.126898
where ρ = (cbrt[9-sqrt(69)]+cbrt[9+sqrt(69)])/cbrt(18) = 1.324718 is the plastic number, the only real solution of x3-x-1=0
Vertex figure [5/3,33,5,3]
External
links
hedrondude   wikipedia  

All, the icosahedral triangles, the pentagrams, and the pentagons, coincide by their face planes pairwise each. So either all are considered separately (type A); or triangle pairs are considered as (rotated) compounds while the other are considered separately (type B); or pentagram pairs are considered as (rotated) compounds while the other are considered separately (type C); or pentagon pairs are considered as (rotated) compounds while the other are considered separately (type D); or both, triangle pairs and pentagram pairs, are considered as compounds (type E); or both, triangle pairs and pentagon pairs, are considered as compounds (type F); or both, pentagram pairs and pentagon pairs, are considered as compounds (type G); or all are considered as compounds each (type H).


Incidence matrix

(Type A)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   3 |   3   0   0 |   * 40  *  * || 1
   5 |   0   5   0 |   *  * 24  * || 1
   5 |   0   0   5 |   *  *  * 24 || 1
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

(Type B)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   6 |   6   0   0 |   * 20  *  * || 2
   5 |   0   5   0 |   *  * 24  * || 1
   5 |   0   0   5 |   *  *  * 24 || 1
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

(Type C)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   3 |   3   0   0 |   * 40  *  * || 1
  10 |   0  10   0 |   *  * 12  * || 2
   5 |   0   0   5 |   *  *  * 24 || 1
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

(Type D)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   3 |   3   0   0 |   * 40  *  * || 1
   5 |   0   5   0 |   *  * 24  * || 1
  10 |   0   0  10 |   *  *  * 12 || 2
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

(Type E)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   6 |   6   0   0 |   * 20  *  * || 2
  10 |   0  10   0 |   *  * 12  * || 2
   5 |   0   0   5 |   *  *  * 24 || 1
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

(Type F)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   6 |   6   0   0 |   * 20  *  * || 2
   5 |   0   5   0 |   *  * 24  * || 1
  10 |   0   0  10 |   *  *  * 12 || 2
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

(Type G)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   3 |   3   0   0 |   * 40  *  * || 1
  10 |   0  10   0 |   *  * 12  * || 2
  10 |   0   0  10 |   *  *  * 12 || 2
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

(Type H)

 120 |   2   2   2 |   3  1  1  1 || 1
-----+-------------+--------------++--
   2 | 120   *   * |   1  1  0  0 || 1
   2 |   * 120   * |   1  0  1  0 || 1
   2 |   *   * 120 |   1  0  0  1 || 1
-----+-------------+--------------++--
   3 |   1   1   1 | 120  *  *  * || 1
   6 |   6   0   0 |   * 20  *  * || 2
  10 |   0  10   0 |   *  * 12  * || 2
  10 |   0   0  10 |   *  *  * 12 || 2
-----+-------------+--------------++--
 60 |  60  60  60 |  60 20 12 12 || 2

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