Rhombihyperhombicosicosahedron

Rhombihyperhombicosicosahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Rahrie
Elements
Components	5 small cubicuboctahedra
Faces	40 triangles as 20 hexagrams, 30 squares, 30 octagons
Edges	120+120
Vertices	120
Vertex figure	Crossed isosceles trapezoid, edge lengths 1, √2+√2, √2, √2+√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{5+2\sqrt2}}{2} \approx 1.39897$
Volume	$10\frac{3+4\sqrt2}{3} \approx 28.85618$
Dihedral angles	8–4: 90°
	8–3: $\arccos\left(\frac{\sqrt3}{3}\right) \approx 54.73561^\circ$
Central density	10
Number of external pieces	1470
Level of complexity	112
Related polytopes
Army	Semi-uniform Grid
Regiment	Rasseri
Dual	Compound of five small hexacronic icositetrahedra
Conjugate	Rhombiquasihyperrhombicosicosahedron
Convex core	Rhombic triacontahedron
Abstract & topological properties
Flag count	960
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

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.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#16).

• Klitzing, Richard. "rahrie".

• Wikipedia Contributors. "Compound of five small cubicuboctahedra".