Trigonal trapezohedral honeycomb
The trigonal trapezohedral honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. Cells are identical trigonal trapezohedron or rhombohedra. John Horton Conway calls it an oblate cubille.
|Trigonal trapezohedral honeycomb|
|Type||Dual uniform honeycomb|
(1/4 of rhombic dodecahedron)
|Space group||Fd3m (227)|
|Coxeter group||×2, [[3]] (double)|
|Dual||Quarter cubic honeycomb|
Related honeycombs and tilings
rhombic dodecahedral honeycomb
Rhombic dodecahedra dissection
It is analogous to the regular hexagonal being dissectable into 3 rhombi and tiling the plane as a rhombille. The rhombille tiling is actually an orthogonal projection of the trigonal trapezohedral honeycomb. A different orthogonal projection produces the quadrille where the rhombi are distorted into squares.
It is dual to the quarter cubic honeycomb with tetrahedral and truncated tetrahedral cells:
- 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, p 292-298, includes all the nonprismatic forms)
- Branko Grünbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49 - 56.