Truncated cubic honeycomb
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Truncated cubic honeycomb | |
---|---|
Rank | 4 |
Type | uniform |
Space | Euclidean |
Notation | |
Bowers style acronym | Tich |
Coxeter diagram | x4x3o4o () |
Elements | |
Cells | N octahedra, N truncated cubes |
Faces | 8N triangles, 3N octagons |
Edges | 3N+12N |
Vertices | 6N |
Vertex figure | Square pyramid, edge lengths 1 (base) and √2+√2 (sides) |
Measures (edge length 1) | |
Vertex density | |
Dual cell volume | |
Related polytopes | |
Army | Tich |
Regiment | Tich |
Dual | Square pyramidal honeycomb |
Conjugate | Quasitruncated cubic honeycomb |
Topological properties | |
Orientable | Yes |
Properties | |
Symmetry | R_{4} |
Convex | Yes |
The truncated cubic honeycomb, or tich, is a convex uniform honeycomb. 1 octahedron and 4 truncated cubes join at each vertex of this honeycomb. As the name suggests, it is the truncation of the cubic honeycomb.
Vertex coordinates[edit | edit source]
The vertices of a truncated cubic honeycomb of edge length 1 are given by all permutations of:
Where i, j, and k range over the integers.
Representations[edit | edit source]
A truncated cubic honeycomb has the following Coxeter diagrams:
- x4x3o4o (regular)
- o3x3o *b4x (S4 symmetry)
- wx4xo3ox4xw&#zx
Gallery[edit | edit source]
Related polytopes[edit | edit source]
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Cubic honeycomb | chon | {4,3,4} | ||
Truncated cubic honeycomb | tich | t{4,3,4} | ||
Rectified cubic honeycomb | rich | r{4,3,4} | ||
Bitruncated cubic honeycomb | batch | 2t{4,3,4} | ||
Rectified cubic honeycomb | rich | r{4,3,4} | ||
Truncated cubic honeycomb | tich | t{4,3,4} | ||
Cubic honeycomb | chon | {4,3,4} | ||
Small rhombated cubic honeycomb | srich | rr{4,3,4} | ||
Great rhombated cubic honeycomb | grich | tr{4,3,4} | ||
Small rhombated cubic honeycomb | srich | rr{4,3,4} | ||
Great rhombated cubic honeycomb | grich | tr{4,3,4} | ||
Small prismated cubic honeycomb = Cubic honeycomb | chon | t_{0,3}{4,3,4} | ||
Prismatorhombated cubic honeycomb | prich | t_{0,1,3}{4,3,4} | ||
Prismatorhombated cubic honeycomb | prich | t_{0,1,3}{4,3,4} | ||
Great prismated cubic honeycomb | gippich | t_{0,1,2,3}{4,3,4} |
External links[edit | edit source]
- Klitzing, Richard. "tich".
- Wikipedia Contributors. "Truncated cubic honeycomb".
- Binnendyk, Eric. "Category 2: Truncates" (#14).