Acronym | rhote (old: rattic) |
Name |
rhombic triacontahedron, terminally chamfered dodecahedron, terminally chamfered icosahedron, surtegmated dodecahedron, surtegmated icosahedron |
© © | |
Inradius | sqrt[(5+2 sqrt(5))/5] = 1.376382 |
Vertex figure | [r5], [R3] |
Dual | id |
Dihedral angles
(at margins) |
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Face vector | 32, 60, 30 |
Confer |
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External links |
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
o3m5o = ao3oo5ob&#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. | 12 * | 5 | 5 [r5] .o3.o5.o | * 20 | 3 | 3 [R3] -------------+-------+----+--- oo3oo5oo&#x | 1 1 | 60 | 2 -------------+-------+----+--- ao .. ob&#zx | 2 2 | 4 | 30 {(r,R)2}
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