# Rhombihyperhombicosicosahedron

Rhombihyperhombicosicosahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymRahrie
Elements
Components5 small cubicuboctahedra
Faces40 triangles as 20 hexagrams, 30 squares, 30 octagons
Edges120+120
Vertices120
Vertex figureCrossed isosceles trapezoid, edge lengths 1, 2+2, 2, 2+2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{5+2\sqrt2}}{2} \approx 1.39897}$
Volume${\displaystyle 10\frac{3+4\sqrt2}{3} \approx 28.85618}$
Dihedral angles8–4: 90°
8–3: ${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) \approx 54.73561^\circ}$
Central density10
Number of external pieces1470
Level of complexity112
Related polytopes
ArmySemi-uniform Grid
RegimentRasseri
DualCompound of five small hexacronic icositetrahedra
ConjugateRhombiquasihyperrhombicosicosahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count960
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The rhombihyperhombicosicosahedron, rahrie, or compound of five small cubicuboctahedra is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams), 30 squares, and 30 octagons, with one triangle, one square, and two octagons joining at each vertex.

It can be formed by replacing each small rhombicuboctahedron in the rhombisnub rhombicosicosahedron with the small cubicuboctahedron with which it shares its edge skeleton.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rhombisnub rhombicosicosahedron.