Acronym dissid
Name disnub icosidodecahedron,
compound of 2 snid
 
 © ©
Vertex figure [34,5]
Dihedral angles
(at margins)
  • between {3} and {3}:   ≈164.18°
  • between {3} and {5}:   ≈152.93°
External
links
hedrondude   wikipedia   polytopewiki  

Both, the icosahedral triangles and the (dodecahedral) pentagons coincide by their face planes pairwise. So either all are considered separately (type A), or triangle pairs are considered as (rotated) compounds while pentagons are considered separately (type B), or conversely pentagons pairs are considered as (rotated) compounds while triangles are considered separately (type C), or both are considered as compounds (type D).


Incidence matrix according to Dynkin symbol

β3β5β   (Type A)

both( . . . ) | 120 |  2   2   2 |  1  1   3 || 1
--------------+-----+------------+-----------++--
both( s 2 s ) |   2 | 60   *   * |  0  0   2 || 1
sefa( β3β . ) |   2 |  * 120   * |  1  0   1 || 1
sefa( . β5β ) |   2 |  *   * 120 |  0  1   1 || 1
--------------+-----+------------+-----------++--
both( s3s . ) |   3 |  0   3   0 | 40  *   * || 1
both( . s5s ) |   5 |  0   0   5 |  * 24   * || 1
sefa( β3β4β ) |   3 |  1   1   1 |  *  * 120 || 1
--------------+-----+------------+-----------++--
both( s3s5s )   60 | 30  60  60 | 20 12  60 || 2

β3β5β   (Type B)

both( . . . ) | 120 |  2   2   2 |  1  1   3 || 1
--------------+-----+------------+-----------++--
both( s 2 s ) |   2 | 60   *   * |  0  0   2 || 1
sefa( β3β . ) |   2 |  * 120   * |  1  0   1 || 1
sefa( . β5β ) |   2 |  *   * 120 |  0  1   1 || 1
--------------+-----+------------+-----------++--
      β3β .   |   6 |  0   6   0 | 20  *   * || 2
both( . s5s ) |   5 |  0   0   5 |  * 24   * || 1
sefa( β3β4β ) |   3 |  1   1   1 |  *  * 120 || 1
--------------+-----+------------+-----------++--
both( s3s5s )   60 | 30  60  60 | 20 12  60 || 2

β3β5β   (Type C)

both( . . . ) | 120 |  2   2   2 |  1  1   3 || 1
--------------+-----+------------+-----------++--
both( s 2 s ) |   2 | 60   *   * |  0  0   2 || 1
sefa( β3β . ) |   2 |  * 120   * |  1  0   1 || 1
sefa( . β5β ) |   2 |  *   * 120 |  0  1   1 || 1
--------------+-----+------------+-----------++--
both( s3s . ) |   3 |  0   3   0 | 40  *   * || 1
      . β5β   |  10 |  0   0  10 |  * 12   * || 2
sefa( β3β4β ) |   3 |  1   1   1 |  *  * 120 || 1
--------------+-----+------------+-----------++--
both( s3s5s )   60 | 30  60  60 | 20 12  60 || 2

β3β5β   (Type D)

both( . . . ) | 120 |  2   2   2 |  1  1   3 || 1
--------------+-----+------------+-----------++--
both( s 2 s ) |   2 | 60   *   * |  0  0   2 || 1
sefa( β3β . ) |   2 |  * 120   * |  1  0   1 || 1
sefa( . β5β ) |   2 |  *   * 120 |  0  1   1 || 1
--------------+-----+------------+-----------++--
      β3β .   |   6 |  0   6   0 | 20  *   * || 2
      . β5β   |  10 |  0   0  10 |  * 12   * || 2
sefa( β3β4β ) |   3 |  1   1   1 |  *  * 120 || 1
--------------+-----+------------+-----------++--
both( s3s5s )   60 | 30  60  60 | 20 12  60 || 2

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