Cuboctahedron atop truncated cube
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Cuboctahedron atop truncated cube | |
---|---|
Rank | 4 |
Type | Segmentotope |
Notation | |
Bowers style acronym | Coatic |
Coxeter diagram | ox4xx3oo&#x |
Elements | |
Cells | 8 triangular prisms, 6 square cupolas, 1 cuboctahedron, 1 truncated cube |
Faces | 8+8+12 triangles, 6+24 squares, 6 octagons |
Edges | 12+24+24+24 |
Vertices | 12+24 |
Vertex figures | 12 wedges, edge lengths 1 (two edges of base and top edge) and √2 (rest of edges) |
24 sphenoids, edge lengths 1, √2, and √2+√2 (2 each) | |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Co–3–trip: 150° |
Squacu–4–trip: | |
Co–4–squacu: 135° | |
Squacu–3–squacu: 120° | |
Tic–8–squacu: 45° | |
Tic–3–trip: 30° | |
Height | |
Central density | 1 |
Related polytopes | |
Army | Coatic |
Regiment | Coatic |
Dual | Rhombic dodecahedral-triakis octahedral tegmoid |
Conjugate | Cuboctahedron atop quasitruncated hexahedron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B3×I, order 48 |
Convex | Yes |
Nature | Tame |
Cuboctahedron atop truncated cube, or coatic, is a CRF segmentochoron (designated K-4.129 on Richard Klitzing's list). As the name suggests, it consists of a cuboctahedron and a truncated cube as bases, connected by 8 triangular prisms and 6 square cupolas.
It can be obtained as a cap of the small rhombated icositetrachoron, which can be obtained by attaching 8 of these segmentochora to the truncated cubic cells of the prismatorhombated hexadecachoron.
Vertex coordinates[edit | edit source]
The vertices of a cuboctahedron atop truncated cube segmentochoron of edge length 1 are given by:
- and all permutations of first three coordinates
- and all permutations of first three coordinates
External links[edit | edit source]
- Klitzing, Richard. "coatic".
- Quickfur. "Cuboctahedron atop Truncated Cube".