Acronym | gike |
TOCID symbol | J, s*O, s*TT |
Name |
great icosahedron, retrosnub tetrahedron, retrosnub tetratetrahedron, edgified penta-stellahedron, vertex figure of gax |
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Circumradius | sqrt[(5-sqrt(5))/8] = 0.587785 |
Inradius | sqrt[(7-3 sqrt(5))/24] = 0.110264 |
Density | 7 |
Vertex figure | [35]/2 |
Lace city in approx. ASCII-art |
o o x v v x o o |
Coordinates |
(1/2, v/2, 0) & even permutations, all changes of sign where v = (sqrt(5)-1)/2 |
General of army | ike |
Colonel of regiment | sissid |
Dual | gissid |
Dihedral angles |
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Face vector | 12, 30, 20 |
Confer |
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External links |
As abstract polytope gike is isomorphic to ike, thereby replacing vertex figure pentagrams by corresponding pentagons. – As such gike is a lieutenant.
This polyhedron is an edge-faceting of the small stellated dodecahedron (sissid).
Incidence matrix according to Dynkin symbol
o5/2o3x . . . | 12 | 5 | 5 --------+----+----+--- . . x | 2 | 30 | 2 --------+----+----+--- . o3x | 3 | 3 | 20 snubbed forms: o5/2o3β
o5/3o3x . . . | 12 | 5 | 5 --------+----+----+--- . . x | 2 | 30 | 2 --------+----+----+--- . o3x | 3 | 3 | 20
x3/2o5/2o . . . | 12 | 5 | 5 ----------+----+----+--- x . . | 2 | 30 | 2 ----------+----+----+--- x3/2o . | 3 | 3 | 20
x3/2o5/3o . . . | 12 | 5 | 5 ----------+----+----+--- x . . | 2 | 30 | 2 ----------+----+----+--- x3/2o . | 3 | 3 | 20
s3/2s3/2s demi( . . . ) | 12 | 1 2 2 | 1 1 3 ------------------+----+---------+------- s 2 s | 2 | 6 * * | 0 0 2 sefa( s3/2s . ) | 2 | * 12 * | 1 0 1 sefa( . s3/2s ) | 2 | * * 12 | 0 1 1 ------------------+----+---------+------- s3/2s . ♦ 3 | 0 3 0 | 4 * * . s3/2s ♦ 3 | 0 0 3 | * 4 * sefa( s3/2s3/2s ) | 3 | 1 1 1 | * * 12
or demi( . . . ) | 12 | 1 4 | 2 3 ----------------------------------------+----+------+----- s 2 s | 2 | 6 * | 0 2 sefa( s3/2s . ) & sefa( . s3/2s ) | 2 | * 24 | 1 1 ----------------------------------------+----+------+----- s3/2s . & . s3/2s ♦ 3 | 0 3 | 8 * sefa( s3/2s3/2s ) | 3 | 1 2 | * 12 starting figure: x3/2x3/2x
s3/2s4o demi( . . . ) | 12 | 1 4 | 2 3 ----------------+----+------+----- . s4o | 2 | 6 * | 0 2 sefa( s3/2s . ) | 2 | * 24 | 1 1 ----------------+----+------+----- s3/2s . ♦ 3 | 0 3 | 8 * sefa( s3/2s4o ) | 3 | 1 2 | * 12 starting figure: x3/2x4o
s3/2s4/3o demi( . . . ) | 12 | 1 4 | 2 3 ------------------+----+------+----- . s4/3o | 2 | 6 * | 0 2 sefa( s3/2s . ) | 2 | * 24 | 1 1 ------------------+----+------+----- s3/2s . ♦ 3 | 0 3 | 8 * sefa( s3/2s4/3o ) | 3 | 1 2 | * 12 starting figure: x3/2x4/3o
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