Webbed space
Webbed space | |
---|---|
Type | Dual uniform honeycomb |
Coxeter–Dynkin diagrams | Template:CDD |
Cell | Square bipyramids |
Faces | Triangles |
Space group Fibrifold notation |
PmTemplate:Overlinem (221) 4−:2 |
Coxeter group | , [4,3,4] |
vertex figures | Template:CDD, Template:CDD |
Dual | Rectified cubic honeycomb |
Properties | Cell-transitive, Face-transitive |
The square bipyramidal honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. John Horton Conway calls it an oblate octahedrille.
It can be seen as a cubic honeycomb with each cube subdivided by a center point into 6 elongated square pyramid cells. The the original cubic honeycomb walls are removed, joining pairs of square pyramids into elongated square bipyramids (octahedron). Its vertex and edge framework is identical to the hexakis cubic honeycomb.
There is one type of plane with faces: a flattended triangular tiling with half of the triangles as holes. These cut face-diagonally through the original cubes. There are also square tiling plane that exist as nonface holes passing through the centers of the octahedral cells.
Tiling plane |
Square tiling "holes" |
flattened triangular tiling |
---|---|---|
Symmetry | p4m, [4,4] (*442) | pmm, [∞,2,∞] (*2222) |
Related honeycombs
It is dual to the rectified cubic honeycomb with octahedral and cuboctahedral cells:
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.