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|Bowers style acronym||Arie|
|Faces||40 triangles as 20 hexagrams, 30 squares|
|Vertex figure||Rectangle, edge lengths 1 and √2|
|Measures (edge length 1)|
|Number of external pieces||260|
|Level of complexity||14|
|Dual||Compound of five rhombic dodecahedra|
|Convex core||Rhombic triacontahedron|
|Abstract & topological properties|
|Symmetry||H3, order 120|
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]
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]
- Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#12).
- Klitzing, Richard. "arie".
- Wikipedia Contributors. "Compound of five cuboctahedra".