Cubic-triangular tiling honeycomb

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In hyperbolic 3-space, the cubic-triangular tiling honeycomb fills space with three kinds of cells: cubes, triangular tiling pieces, and cuboctahedra. Around each vertex, the pattern matches the rhombitrihexagonal arrangement. It is named for its two regular cell types. A honeycomb fills space with polyhedra so there are no gaps, and this idea applies in any number of dimensions. Most honeycombs live in flat (Euclidean) space, but they can also exist in curved spaces like hyperbolic space. If you project any finite uniform polytope onto a circumsphere, you get a uniform honeycomb on the sphere.