Acronym | erhote |
Name | expanded rhombic triacontahedron |
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Vertex figure | [4,5,4,r], [4,3,4,R] |
Face vector | 120, 240, 122 |
Confer | |
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The rhombs {(r,R)2} have vertex angles r = arccos(1/sqrt(5)) = 63.434949° resp. R = arccos(-1/sqrt(5)) = 116.565051°. Esp. rr : RR = (1+sqrt(5))/2.
All a = rr and b = RR edges, provided in the below description, only qualify as pseudo edges wrt. the full polyhedron. Edge size used here is rR = x = 1.
Incidence matrix according to Dynkin symbol
ao3xx5ob&#zx → height = 0 a = rr = 2 sqrt[(5+sqrt(5))/10] = 1.701302, b = RR = 2 sqrt[(5-sqrt(5))/10] = 1.051462 o.3o.5o. | 60 * | 2 2 0 | 1 1 2 0 [4,5,4,r] .o3.o5.o | * 60 | 0 2 2 | 0 1 2 1 [4,3,4,R] -------------+-------+-----------+------------ .. x. .. | 2 0 | 60 * * | 1 0 1 0 oo3oo5oo&#x | 1 1 | * 120 * | 0 1 1 0 .. .x .. | 0 2 | * * 60 | 0 0 1 1 -------------+-------+-----------+------------ .. x.5o. | 5 0 | 5 0 0 | 12 * * * ao .. ob&#zx | 2 2 | 0 4 0 | * 30 * * {(r,R)2} .. xx ..&#x | 2 2 | 1 2 1 | * * 60 * .o3.x .. | 0 3 | 0 0 3 | * * * 20
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