Triangular tiling honeycomb The omnitruncated triangular tiling honeycomb, , has truncated trihexagonal tiling and hexagonal prism cells, with a tetrahedron vertex figure. The runcisnub triangular tiling honeycomb, , has trihexagonal tiling, triangular tiling, triangular prism, and triangular cupola cells. It is vertex-transitive, but not uniform, since it contains Johnson solid triangular cupola cells. Triangular tiling honeycomb The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. It is called "paracompact" because it has infinite cells and vertex figures, with all vertices as ideal points at infinity. It has Schläfli symbol {3,6,3}, being composed of triangular tiling
Cubic honeycomb and its dual triangular pyramidille. Four cells exist around each vertex: The "cantitruncated cubic honeycomb" can be orthogonally projected into the euclidean plane with various symmetry arrangements. Cells can be shown in two different symmetries. The linear Coxeter diagram form can be drawn with one color for each cell type. The bifurcating diagram form can be drawn with two types (colors) of truncated cuboctahedron cells alternating. The dual of the "cantitruncated cubic honeycomb" is called a triangular pyramidille, with Coxeter diagram, . This honeycomb cells represents the fundamental domains of formula_2 symmetry. A cell can be as 1/24 of a