Acronym | ... |
Name |
3ike+3gad (?), 3cid (?) |
Circumradius | sqrt[(5+sqrt(5))/8] = 0.951057 |
Vertex figure |
3[(3,5)3] (type A) 3[(3/2,5)3] (type B) |
General of army | ike |
Colonel of regiment | ike |
Confer |
Looks like a compound of 3 icosahedra (ike) and 3 great dodecahedron (gad), and indeed vertices coincide by 3, edges coincide by 6, both face types coincide by 3 each.
It occurs in 2 types: either triangles and pentagon cycle in the same direction (type A), or in opposite direction (type B).
Incidence matrix according to Dynkin symbol
s5/4s5s5*a (type A) demi( . . . ) | 60 | 2 2 2 | 1 1 1 3 -------------------+----+----------+------------ sefa( s5/4s . ) | 2 | 60 * * | 1 0 0 1 sefa( s . s5*a ) | 2 | * 60 * | 0 1 0 1 sefa( . s5s ) | 2 | * * 60 | 0 0 1 1 -------------------+----+----------+------------ s5/4s . ♦ 5 | 5 0 0 | 12 * * * s . s5*a | 5 | 0 5 0 | * 12 * * . s5s | 5 | 0 0 5 | * * 12 * sefa( s5/4s5s5*a ) | 3 | 1 1 1 | * * * 60 starting figure: x5/4x5x5*a
s5/4s5/4s5/4*a (type B) demi( . . . ) | 60 | 2 2 2 | 1 1 1 3 -----------------------+----+----------+------------ sefa( s5/4s . ) | 2 | 60 * * | 1 0 0 1 sefa( s . s5/4*a ) | 2 | * 60 * | 0 1 0 1 sefa( . s5/4s ) | 2 | * * 60 | 0 0 1 1 -----------------------+----+----------+------------ s5/4s . ♦ 5 | 5 0 0 | 12 * * * s . s5/4*a ♦ 5 | 0 5 0 | * 12 * * . s5/4s ♦ 5 | 0 0 5 | * * 12 * sefa( s5/4s5/4s5/4*a ) | 3 | 1 1 1 | * * * 60 starting figure: x5/4x5/4x5/4*a
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