Acronym ...
Name pyritohedally expanded icosidodecahedron
 
 
Vertex figure [3,R,4,R], [4,r,5,r], [3,5,h,r], [5,H,R]
Face vector 72, 132, 62

The vertex angles of the shield-hexagons {(h,H)3} are h = arccos[-(3-sqrt(5))/sqrt(32)] = 97.761244° resp. H = arccos[-sqrt(5/8)] = 142.238756°, while those of the rhombs {(r,R)2} are r = arccos[(sqrt(5)-1)/sqrt(32)] = 77.378584° resp. R = arccos[-(sqrt(5)-1)/sqrt(32)] = 102.621416°.


Incidence matrix according to Dynkin symbol

12  *  *  * |  2  2  0  0  0  0 | 1  1  2  0 0  [3,R,4,R]
 * 12  *  * |  2  0  2  0  0  0 | 1  0  2  1 0  [4,r,5,r]
 *  * 24  * |  0  1  0  1  1  1 | 0  1  1  1 1  [3,5,h,r]
 *  *  * 24 |  0  0  1  0  1  1 | 0  0  1  1 1  [5,H,R]
------------+-------------------+-------------
 1  1  0  0 | 24  *  *  *  *  * | 1  0  1  0 0
 1  0  1  0 |  * 24  *  *  *  * | 0  1  1  0 0
 0  1  0  1 |  *  * 24  *  *  * | 0  0  1  1 0
 0  0  2  0 |  *  *  * 12  *  * | 0  1  0  1 0
 0  0  1  1 |  *  *  *  * 24  * | 0  0  1  0 1
 0  0  1  1 |  *  *  *  *  * 24 | 0  0  0  1 1
------------+-------------------+-------------
 2  2  0  0 |  4  0  0  0  0  0 | 6  *  *  * *  {4}
 1  0  2  0 |  0  2  0  1  0  0 | * 12  *  * *  {3}
 1  1  1  1 |  1  1  1  0  1  0 | *  * 24  * *  {(r,R)2}
 0  1  2  2 |  0  0  2  1  0  2 | *  *  * 12 *  {5}
 0  0  3  3 |  0  0  0  0  3  3 | *  *  *  * 8  {(h,H)3}

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