Great prismated cubic honeycomb
Great prismated cubic honeycomb | |
---|---|
Rank | 4 |
Type | uniform |
Space | Euclidean |
Notation | |
Bowers style acronym | Gippich |
Coxeter diagram | x4x3x4x () |
Elements | |
Cells | 3N octagonal prisms, N great rhombicuboctahedra |
Faces | 6N+12N squares, 8N hexagons, 6N octagons |
Edges | 24N+24N |
Vertices | 24N |
Vertex figure | Phyllic disphenoid, edge lengths √2 (3), √3 (2), and √2+√2 (1) |
Measures (edge length 1) | |
Vertex density | |
Dual cell volume | |
Related polytopes | |
Army | Gippich |
Regiment | Gippitch |
Dual | Phyllic disphenoidal honeycomb |
Conjugate | Quasiquasiprismated cubic honeycomb |
Topological properties | |
Orientable | Yes |
Properties | |
Symmetry | R_{4}×2 |
Convex | Yes |
The great prismated cubic honeycomb, or gippich, also known as the omnitruncated cubic honeycomb, or otch, is a convex uniform honeycomb. 2 great rhombicuboctahedra and 2 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the omnitruncate of the R4 family.
This honeycomb can be alternated into a snub bicubic honeycomb, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create an edge-snub cubic honeycomb, cantic bisnub cubic honeycomb or great birhombitetrahedral honeycomb, which are nonuniform.
Vertex coordinates[edit | edit source]
The vertices of a great prismated 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. "gippich".
- Wikipedia Contributors. "Omnitruncated cubic honeycomb".
- Binnendyk, Eric. "Category 5: Greater Truncates" (#99).