| Acronym | ... |
| Name | pyritohedally expanded icosidodecahedron |
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| 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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