Acronym | siddo |
Name |
snub disoctahedron, octahedral compound of 2 ike, vertex figure of sody |
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Circumradius | sqrt[(5+sqrt(5))/8] = 0.951057 |
Inradius | sqrt[(7+3 sqrt(5))/24] = 0.755761 |
Coordinates |
(τ/2, 1/2, 0) & all permutations, all changes of sign where τ = (1+sqrt(5))/2 |
Vertex figure | [35] |
General of army | x3f4o |
Colonel of regiment | (is itself locally convex) |
Dihedral angles
(at margins) |
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External links |
Faces of an octahedral subset of triangles pairwise fall into coincident face planes. So either those can be considered separately (type A); or they are considered as (rotated) 2-triangle-compounds (type B).
The right pic above displays a coloring induced as outer symmetry when being used as vertex figure of sody (for further details see there).
Incidence matrix according to Dynkin symbol
β3β4o (Type A) both( . . . ) | 24 | 1 4 | 2 3 || 1 -----------------+----+-------+-------++-- both( . s4o ) | 2 | 12 * | 0 2 || 1 sefa( β3β . ) & | 2 | * 48 | 1 1 || 1 -----------------+----+-------+-------++-- both( s3s . ) & | 3 | 0 3 | 16 * || 1 sefa( β3β4o ) | 3 | 1 2 | * 24 || 1 -----------------+----+-------+-------++-- both( s3s4o ) ♦ 12 | 6 24 | 8 12 || 2 starting figure: x3x4o
β3β4o (Type B) both( . . . ) | 24 | 1 4 | 2 3 || 1 -----------------+----+-------+------++-- both( . s4o ) | 2 | 12 * | 0 2 || 1 sefa( β3β . ) & | 2 | * 48 | 1 1 || 1 -----------------+----+-------+------++-- β3β . & | 6 | 0 6 | 8 * || 2 sefa( β3β4o ) | 3 | 1 2 | * 24 || 1 -----------------+----+-------+------++-- both( s3s4o ) ♦ 12 | 6 24 | 8 12 || 2 starting figure: x3x4o
β3β3β (Type A) both( . . . ) | 24 | 1 4 | 2 3 || 1 -----------------+----+-------+-------++-- both( s 2 s ) | 2 | 12 * | 0 2 || 1 sefa( β3β . ) & | 2 | * 48 | 1 1 || 1 -----------------+----+-------+-------++-- both( s3s . ) & | 3 | 0 3 | 16 * || 1 sefa( β3β3β ) | 3 | 1 2 | * 24 || 1 -----------------+----+-------+-------++-- both( s3s3s ) ♦ 12 | 6 24 | 8 12 || 2 starting figure: x3x3x
β3β3β (Type B) both( . . . ) | 24 | 1 4 | 2 3 || 1 -----------------+----+-------+------++-- both( s 2 s ) | 2 | 12 * | 0 2 || 1 sefa( β3β . ) & | 2 | * 48 | 1 1 || 1 -----------------+----+-------+------++-- β3β . & | 6 | 0 6 | 8 * || 2 sefa( β3β3β ) | 3 | 1 2 | * 24 || 1 -----------------+----+-------+------++-- both( s3s3s ) ♦ 12 | 6 24 | 8 12 || 2 starting figure: x3x3x
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