Snub pseudosnub rhombicosahedron

Snub pseudosnub rhombicosahedron
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sapisseri
Elements
Components	20 tetrahemihexahedra
Faces	20+60 triangles, 60 squares
Edges	60+60+120
Vertices	60
Vertex figure	Compound of two bowties, edge lengths 1 and √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2} ≈ 0.70711$
Dihedral angle	$\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$
Central density	even
Related polytopes
Army	Semi-uniform Srid
Regiment	Gidrid
Dual	Compound of twenty tetrahemihexacrons
Conjugate	Snub psuedosnub rhombicosahedron
Abstract & topological properties
Orientable	No
Properties
Symmetry	H3+, order 60
Convex	No
Nature	Tame

The snub pseudosnub rhombicosahedron, sapisseri, or compound of twenty tetrahemihexahedra is a biformic polyhedron compound. It consists of 20+60 triangles and 60 squares. The vertices coincide in pairs, and thus four triangles and four squares join at each vertex. If the vertices are considered as single compound vertices, this compound is uniform. If they are considered as two separate vertices, it has two vertex orbits.

This compound can be formed by replacing each octahedron in the disnub icosahedron with the tetrahemihexahedron with which it shares its edges. Therefore, it also has the same edges as the great dirhombicosidodecahedron, although it is chiral, unlike either the great dirhombicosidodecahedron or disnub icosahedron.

It can be constructed as a blend of the great dirhombicosidodecahedron and the great snub dodecicosidodecahedron.

Vertex coordinates

Its vertices are the same as those of the disnub icosahedron.

External links

• Bowers, Jonathan. "Polyhedron Category C9: Octahedral Continuums" (#67).

• Klitzing, Richard. "sapisseri".

• Wikipedia Contributors. "Compound of twenty tetrahemihexahedra".