Square tiling honeycomb
(Redirected from Order-3 square tiling honeycomb)
Square tiling honeycomb | |
---|---|
Rank | 4 |
Type | Regular, paracompact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Squah |
Coxeter diagram | x4o4o3o () |
Schläfli symbol | {4,4,3} |
Elements | |
Cells | 6N square tilings |
Faces | 3NM squares |
Edges | 4NM |
Vertices | NM |
Vertex figure | Cube, edge length √2 |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Squah |
Regiment | Squah |
Dual | Octahedral honeycomb |
Abstract & topological properties | |
Flag count | 48NM |
Orientable | Yes |
Properties | |
Symmetry | [4,4,3] |
Convex | Yes |
The order-3 square tiling honeycomb or just square tiling honeycomb is a paracompact regular tiling of 3D hyperbolic space. Each cell is a square tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. 3 square tilings meet at each edge, and 6 meet at each vertex.
It can be formed by rectifying the order-4 square tiling honeycomb.
Representations[edit | edit source]
The square tiling honeycomb has the following Coxeter diagrams:
- x4o4o3o () (full symmetry)
- o4x4o4o () (as rectified order-4 square tiling honeycomb)
- o4x4o2o4*b () (cuboid verf)
- x4o4x2o4*b () (square frustum verf)
- x4o4x4o4*a () (rectangular frustum verf)
External links[edit | edit source]
- Klitzing, Richard. "squah".
- Wikipedia contributors. "Square tiling honeycomb".
- lllllllllwith10ls. "Category 1: Regulars" (#13).
- lllllllllwith10ls. "Category 4: Square Rectates" (#13 - recount under sisquah symmetry).