Compound of five great cubicuboctahedra
(Redirected from Rhombiquasihyperrhombicosicosahedron)
Rhombiquasihyperhomb-icosicosahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Notation | |
Bowers style acronym | Raquahri |
Elements | |
Components | 5 great cubicuboctahedra |
Faces | 40 triangles as 20 hexagrams, 30 squares, 30 octagrams |
Edges | 120+120 |
Vertices | 120 |
Vertex figure | Isosceles trapezoid, edge lengths 1, √2–√2, √2, √2–√2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 8/3–3: |
8/3–4: 90° | |
Central density | 20 |
Number of external pieces | 840 |
Level of complexity | 56 |
Related polytopes | |
Army | Semi-uniform Grid, edge lengths (dipentagon-ditrigon), (dipentagon-rectangle), (ditrigon-rectangle) |
Regiment | Raquahri |
Dual | Compound of five great hexacronic icositetrahedra |
Conjugate | Compound of five small cubicuboctahedra |
Convex core | Rhombic triacontahedron |
Abstract & topological properties | |
Flag count | 960 |
Orientable | Yes |
Properties | |
Symmetry | H3, order 120 |
Convex | No |
Nature | Tame |
The rhombiquasihyperhombicosicosahedron, raquahri, or compound of five great cubicuboctahedra is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams), 30 squares, and 30 octagrams, with one triangle, one square, and two octagrams joining at each vertex.
Gallery[edit | edit source]
Vertex coordinates[edit | edit source]
The vertices of a rhombiquasihyperhombicosicosahedron of edge length 1 can be given by all even permutations of:
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#18).
- Klitzing, Richard. "raquahri".
- Wikipedia contributors. "Compound of five great cubicuboctahedra".