Trigonal trapezohedral honeycomb into squares. It is dual to the quarter cubic honeycomb with tetrahedral and truncated tetrahedral cells: 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. 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
Order-8-3 triangular honeycomb construction as a uniform honeycomb, Schläfli symbol {∞,(8,∞,8)}, Coxeter diagram, , with alternating types or colors of cells. Order-8-3 triangular honeycomb In the geometry of hyperbolic 3-space, the order-8-3 triangular honeycomb (or 3,8,3 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,8,3}. It has three order-8 triangular tiling {3,8} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in an octagonal tiling vertex figure. It is a part of a sequence of regular honeycombs with order-8 triangular tiling cells: {3,8,"p"}. It is a part of