Prismatorhombated cubic honeycomb
Jump to navigation
Jump to search
Prismatorhombated cubic honeycomb | |
---|---|
Rank | 4 |
Type | Uniform |
Space | Euclidean |
Notation | |
Bowers style acronym | Prich |
Coxeter diagram | x4x3o4x () |
Elements | |
Cells | 3N cubes, 3N octagonal prisms, N truncated cubes, N small rhombicuboctahedra |
Faces | 8N triangles, 6N+12N+12N squares, 6N octagons |
Edges | 12N+24N+24N |
Vertices | 24N |
Vertex figure | Isosceles trapezoidal pyramid, base edge lengths 1, √2, √2, √2, side edge lengths √2, √2, √2+√2, √2+√2 |
Measures (edge length 1) | |
Vertex density | |
Dual cell volume | |
Related polytopes | |
Army | Prich |
Regiment | Prich |
Dual | Kite pyramidal honeycomb |
Conjugate | Quasiprismatoquasirhombated cubic honeycomb |
Topological properties | |
Orientable | Yes |
Properties | |
Symmetry | R_{4} |
Convex | Yes |
The prismatorhombated cubic honeycomb, or prich, also known as the runcitruncated cubic honeycomb, is a convex uniform honeycomb. 1 small rhombicuboctahedron, 1 truncated cube, 1 cube, and 2 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the runcitruncation of the cubic honeycomb.
This honeycomb can be subsymmetrically faceted into a runcicantic snub cubic honeycomb, although it cannot be made scaliform.
Vertex coordinates[edit | edit source]
The vertices of a prismatorhombated cubic honeycomb of edge length 1 are given by all permutations of:
where i, j, and k range over the integers.
Gallery[edit | edit source]
Orthogonal projection into Euclidean plane with V3 symmetry
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. "prich".
- Wikipedia Contributors. "Runcitruncated cubic honeycomb".
- Binnendyk, Eric. "Category 6: Prismatorhombates" (#110).