Compound of twenty tetrahemihexahedra

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Compound of twenty tetrahemihexahedra
Rank3
TypeUniform
Notation
Bowers style acronymSapisseri
Elements
Components20 tetrahemihexahedra
Faces20+60 triangles, 60 squares
Edges60+60+120
Vertices60
Vertex figureCompound of two bowties, edge lengths 1 and 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Dihedral angle${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Central densityeven
Related polytopes
ArmySemi-uniform srid, edge lengths ${\displaystyle {\sqrt {\frac {3-{\sqrt {5}}-{\sqrt {10{\sqrt {5}}-22}}}{2}}}}$ (pentagons), ${\displaystyle {\sqrt {\frac {{\sqrt {5}}-1-2{\sqrt {{\sqrt {5}}-2}}}{2}}}}$ (triangles)
RegimentGidrid
DualCompound of twenty tetrahemihexacrons
ConjugateCompound of twenty tetrahemihexahedra
Abstract & topological properties
OrientableNo
Properties
SymmetryH3+, order 60
ConvexNo
NatureTame

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.