In the field of hyperbolic geometry, the order-6 hexagonal tiling honeycomb arises one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is called paracompact because it has infinite cells. Each cell consists of a hexagonal tiling whose vertices lie on a horosphere: a flat plane in hyperbolic space that approaches a single ideal point at infinity. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions.