Truncated octahedron atop great rhombicuboctahedron
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Truncated octahedron atop great rhombicuboctahedron | |
---|---|
Rank | 4 |
Type | Segmentotope |
Notation | |
Bowers style acronym | Toagirco |
Coxeter diagram | ox4xx3xx&#x |
Elements | |
Cells | 12 triangular prisms, 8 hexagonal prisms, 6 square cupolas, 1 truncated octahedron, 1 great rhombicuboctahedron |
Faces | 24 triangles, 6+12+24+24 squares, 8+8 hexagons, 6 octagons |
Edges | 12+24+24+24+24+48 |
Vertices | 24+48 |
Vertex figures | 24 isosceles trapezoidal pyramids, base edge lengths 1, √2, √2, √2; lateral edge lengths √2, √2, √3, √2+√2 |
48 irregular tetrahedra, edge lengths 1 (1), √2 (2), √3 (2), and √2+√2 (1) | |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Hip–4–trip: |
Toe–6–hip: 150° | |
Squacu–3–trip: 150° | |
Squacu–4–hip: | |
Toe–4–squacu: 135° | |
Girco–4–squacu: 60° | |
Girco–4–trip: | |
Girco–6–hip: 30° | |
Height | |
Central density | 1 |
Related polytopes | |
Army | Toagirco |
Regiment | Toagirco |
Dual | Tetrakis hexahedral-disdyakis dodecahedral tegmoid |
Conjugate | Truncated octahedron atop quasitruncated cuboctahedron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B3×I, order 48 |
Convex | Yes |
Nature | Tame |
Truncated octahedron atop great rhombicuboctahedron, or toagirco, is a CRF segmentochoron (designated K-4.149 on Richard Klitzing's list). As the name suggests, it consists of a truncated octahedron and a great rhombicuboctahedron as bases, connected by 12 triangular prisms, 8 hexagonal prisms, and 6 square cupolas.
It can be constructed as a cap of the prismatorhombated icositetrachoron, which can be obtained by attaching 8 of these segmentochora to the great rhombicuboctahedral cells of the great disprismatotesseractihexadecachoron.
Vertex coordinates[edit | edit source]
The vertices of a truncated octahedron atop great rhombicuboctahedron segmentochoron of edge length 1 are given by:
- and all permutations of the first three coordinates,
- and all permutations of the first three coordinates.
External links[edit | edit source]
- Klitzing, Richard. "toagirco".