Small rhombated cubic honeycomb
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Small rhombated cubic honeycomb | |
---|---|
Rank | 4 |
Type | uniform |
Space | Euclidean |
Notation | |
Bowers style acronym | Srich |
Coxeter diagram | x4o3x4o () |
Elements | |
Cells | 3N cubes, N cuboctahedra, N small rhombicuboctahedra |
Faces | 8N triangles, 3N+6N+12N squares |
Edges | 12N+24N |
Vertices | 12N |
Vertex figure | Rectangular wedge, edge lengths 1 (two edges of base) and √2 (remaining edges) |
Measures (edge length 1) | |
Vertex density | |
Dual cell volume | |
Related polytopes | |
Army | Srich |
Regiment | Srich |
Dual | Notch honeycomb |
Conjugate | Quasirhombated cubic honeycomb |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | R_{4} |
Convex | Yes |
The small rhombated cubic honeycomb, or srich, also known as the cantellated cubic honeycomb, is a convex uniform honeycomb. 1 cuboctahedron, 2 small rhombicuboctahedra, and 2 cubes join at each vertex of this honeycomb. As the name suggests, it is the cantellation of the cubic honeycomb.
Vertex coordinates[edit | edit source]
The vertices of a small rhombated 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 small rhombated cubic honeycomb has the following Coxeter diagrams:
- x4o3x4o (regular)
- x3o3x *b4x (S4 symmetry)
- s4x3o4x (as alternated faceting)
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. "srich".
- Wikipedia Contributors. "Cantellated cubic honeycomb".
- Binnendyk, Eric. "Category 4: Sphenoverts" (#71).