Truncated octahedral prism
|Truncated octahedral prism|
|Bowers style acronym||Tope|
|Coxeter diagram||x o4x3x ()|
|Cells||6 cubes, 8 hexagonal prisms, 2 truncated octahedra|
|Faces||12+12+24 squares, 16 hexagons|
|Vertex figure||Sphenoid, edge lengths √2, √3, √3 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of external pieces||16|
|Level of complexity||12|
|Dual||Tetrakis hexahedral tegum|
|Abstract & topological properties|
|Symmetry||B3×A1, order 96|
The truncated octahedral prism or tope is a prismatic uniform polychoron that consists of 2 truncated octahedra, 6 cubes, and 8 hexagonal prisms. Each vertex joins 1 truncated octahedron, 1 cube, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated octahedron. As such it is also a convex segmentochoron (designated K-4.89 on Richard Klitzing's list).
This polychoron can be alternated into a pyritohedral icosahedral antiprism, although it cannot be made uniform.
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, toe atop toe
Vertex coordinates[edit | edit source]
The vertices of a truncated octahedral prism of edge length 1 are given by all permutations of the first three coordinates of:
Representations[edit | edit source]
A truncated octahedral prism has the following Coxeter diagrams:
- x o4x3x (full symmetry)
- x x3x3x () (bases have A3 symmetry)
- s2s4x3x () (bases have A3 symmetry, as snub)
- oo4xx3xx&#x (bases considered separately)
- xx3xx3xx&#x (bases separately under A3)
- xxxxx xuxux4ooqoo&#xt (BC2×A1 axial, cube-first)
- xxxx xuxx3xxux&#xt (A2×A1 axial, hexagonal prism-first)
External links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#900).
- Klitzing, Richard. "Tope".
- Wikipedia Contributors. "Truncated octahedral prism".