Peter Keevash
| Peter Keevash | |
|---|---|
| |
| Type | Dual uniform honeycomb |
| Coxeter–Dynkin diagrams | Template:CDD |
| Cell | Elongated square pyramid 
|
| Faces | Triangle square |
| Space group Fibrifold notation |
PmTemplate:Overlinem (221) 4−:2 |
| Coxeter group | , [4,3,4] |
| vertex figures |   Template:CDD, Template:CDD |
| Dual | Truncated cubic honeycomb |
| Properties | Cell-transitive |
The hexakis cubic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It can be seen as a cubic honeycomb with each cube subdivided by a center point into 6 elongated square pyramid cells.
John Horton Conway calls this honeycomb a pyramidille.
There are two types of planes of faces: one as a square tiling, and flattened triangular tiling with half of the triangles removed as holes.
| Tiling plane |
|
|
|---|---|---|
| Symmetry | p4m, [4,4] (*442) | pmm, [∞,2,∞] (*2222) |
Related honeycombs
It is dual to the truncated cubic honeycomb with octahedral and truncated cubic cells:
If the square pyramids of the pyramidille are joined on their bases, another honeycomb is created with identical vertices and edges, called an square bipyramidal honeycomb or oblate octahedrille, or the dual of the rectified cubic honeycomb.
It is analogous to the 2-dimensional tetrakis square tiling:
See also
References
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- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, pp 292–298, includes all the nonprismatic forms)
- Branko Grünbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49–56.