| bgcolor=#e7dcc3 colspan=2 | Trigonal trapezohedral honeycomb | |
|---|---|---|
| Type | Dual uniform honeycomb | |
| Coxeter-Dynkin diagrams | ||
| Cell | Trigonal trapezohedron (1/4 of rhombic dodecahedron) | |
| Faces | Rhombus | |
| Space group | ||
| Coxeter group | (double) | |
| vertex figures | ||
| Dual | Quarter cubic honeycomb | |
| Properties | Cell-transitive, Face-transitive |
In geometry, the trigonal trapezohedral honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. Cells are identical trigonal trapezohedra or rhombohedra. Conway, Burgiel, and Goodman-Strauss call it an oblate cubille.
This honeycomb can be seen as a rhombic dodecahedral honeycomb, with the rhombic dodecahedra dissected with its center into 4 trigonal trapezohedra or rhombohedra.
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: