Order-6 dodecahedral honeycomb are on the ideal surface. It is one of 15 regular hyperbolic honeycombs in 3-space, 11 of which like this one are paracompact, with infinite cells or vertex figures. There are 15 uniform honeycombs in the [5,3,6] Coxeter group family, including this regular form and its regular dual, order-5 hexagonal tiling honeycomb, {6,3,5}. This honeycomb is a part of a sequence of polychora and honeycombs with triangular tiling vertex figures: This honeycomb is a part of a sequence of regular polytopes and honeycombs with dodecahedral cells: The rectified order-6 dodecahedral honeycomb, t{5,3,6} has icosidodecahedron and triangular tiling cells connected in
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