Compound of five cubohemioctahedra

Compound of five cubohemioctahedra
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Gari
Elements
Components	5 cubohemioctahedra
Faces	30 squares, 20 hexagons as 10 stellated dodecagons
Edges	120
Vertices	60
Vertex figure	Bowtie, edge lengths √2 and √3
Measures (edge length 1)
Circumradius	1
Dihedral angle	$\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Central density	odd
Related polytopes
Army	Semi-uniform Srid, edge lengths ${\frac {3{\sqrt {2}}-{\sqrt {10}}}{4}}$ (pentagons), ${\frac {\sqrt {2}}{2}}$ (triangles)
Regiment	Arie
Dual	Compound of five hexahemioctacrons
Conjugate	Compound of five cubohemioctahedra
Abstract & topological properties
Orientable	No
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great antirhombicosahedron, gari, or compound of five cubohemioctahedra is a uniform polyhedron compound. It consists of 30 squares and 20 hexagons (which pair up into 10 stellated dodecagons), with two of each joining at a vertex.

It can be formed by replacing each cuboctahedron in the antirhombicosicosahedron with the cubohemioctahedron with which it shares its edge skeleton.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#14).

• Klitzing, Richard. "gari".
• Wikipedia contributors. "Compound of five cubohemioctahedra".