Antirhombicosicosahedron

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Antirhombicosicosahedron
UC59-5 cuboctahedra.png
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymArie
Elements
Components5 cuboctahedra
Faces40 triangles as 20 hexagrams, 30 squares
Edges120
Vertices60
Vertex figureRectangle, edge lengths 1 and 2
Measures (edge length 1)
Circumradius1
Volume
Dihedral angle
Central density5
Related polytopes
ArmySemi-uniform Srid
RegimentArie
DualCompound of five rhombic dodecahedra
ConjugateAntirhombicosicosahedron
Convex coreRhombic triacontahedron
Topological properties
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The antirhombicosicosahedron, arie, or compound of five cuboctahedra is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 30 squares, with two of each joining at a vertex.

It can be thought of as a rectification of either the small icosicosahedron or the rhombihedron, or the cantellation of the chiricosahedron.

Its quotient prismatic equivalent is the cuboctahedral pentachoroorthowedge, which is seven-dimensional.

Gallery[edit | edit source]

5co-arie.png

Vertex coordinates[edit | edit source]

The vertices of an antirhombicosicosahedron of edge length 1 can be given by all even permutations of:

External links[edit | edit source]