Compound of five great rhombihexahedra

Compound of five great rhombihexahedra
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Rasquahr
Elements
Components	5 great rhombihexahedra
Faces	60 squares, 30 octagrams
Edges	120+120
Vertices	120
Vertex figure	Butterfly, edge lengths √2 and √2–√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{5-2\sqrt2}}{2} \approx 0.73681$
Dihedral angles	8/3–4 #1: 90°
	8/3–4 #2: 45°
Central density	odd
Related polytopes
Army	Semi-uniform Grid, edge lengths $\frac{-2+\sqrt2+2\sqrt5-\sqrt{10}}{4}$ (dipentagon-ditrigon), $\frac{-4+\sqrt2+\sqrt{10}}{4}$ (dipentagon-rectangle), $\frac{2-\sqrt2}{2}$ (ditrigon-rectangle)
Regiment	Raquahri
Dual	Compound of five great rhombihexacrons
Conjugate	Compound of five small rhombihexahedra
Convex core	Deltoidal hexecontahedron
Abstract & topological properties
Orientable	No
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The rhombisnub quasihyperhombihedron, rasquahr, or compound of five great rhombihexahedra is a uniform polyhedron compound. It consists of 60 squares and 30 octagrams, with two of each joining at a vertex.

It can be formed by replacing each great cubicuboctahedron in the rhombiquasihyperhombicosicosahedron with the great rhombihexahedron with which it shares its edge skeleton.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#20).

• Klitzing, Richard. "rasquahr".

• Wikipedia Contributors. "Compound of five great rhombihexahedra".