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- In the field of hyperbolic geometry, the hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is paracompact because it has cells composed of an infinite number of faces. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. The Schläfli symbol of the hexagonal tiling honeycomb is {6,3,3}. Since that of the hexagonal tiling is {6,3}, this honeycomb has three such hexagonal tilings meeting at each edge. Since the Schläfli symbol of the tetrahedron is {3,3}, the vertex figure of this honeycomb is a tetrahedron. Thus, four hexagonal tilings meet at each vertex of this honeycomb, six hexagons meet at each vertex, and four edges meet at each vertex. (en)
- 在雙曲幾何學中，三階六邊形鑲嵌蜂巢體是一種完全填滿仿緊雙曲空間的幾何結構，是十一種三維仿緊正雙曲密鋪之一，由正六邊形鑲嵌的胞組成。由於其胞為一種無限面體，因此該幾何結構為仿緊空間。 (zh)
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