Alternated hexagonal tiling honeycomb

In three-dimensional hyperbolic geometry, the alternated hexagonal tiling honeycomb, h{6,3,3}, or , is a semiregular tessellation with tetrahedron and triangular tiling cells arranged in an octahedron vertex figure.

A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps.

It has five alternated constructions from reflectional Coxeter groups all with four mirrors and only the first being regular: [6,3,3], [3,6,3], [6,3,6], [6,3[3]] and [3[3,3]] , having 1, 4, 6, 12 and 24 times larger fundamental domains respectively.

The ringed Coxeter diagrams are , , , and , representing different types (colors) of hexagonal tilings in the Wythoff construction.

The runcicantic hexagonal tiling honeycomb, h2,3{6,3,3}, or , has truncated tetrahedron, triangular prism, truncated octahedron, and trihexagonal tiling facets, with a rectangular pyramid vertex figure.