About: Order-6 tetrahedral honeycomb

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In hyperbolic 3-space, the order-6 tetrahedral honeycomb is a paracompact regular space-filling tessellation (or honeycomb). It is paracompact because it has vertex figures composed of an infinite number of faces, and has all vertices as ideal points at infinity. With Schläfli symbol {3,3,6}, the order-6 tetrahedral honeycomb has six ideal tetrahedra around each edge. All vertices are ideal, with infinitely many tetrahedra existing around each vertex in a triangular tiling vertex figure.

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  • In hyperbolic 3-space, the order-6 tetrahedral honeycomb is a paracompact regular space-filling tessellation (or honeycomb). It is paracompact because it has vertex figures composed of an infinite number of faces, and has all vertices as ideal points at infinity. With Schläfli symbol {3,3,6}, the order-6 tetrahedral honeycomb has six ideal tetrahedra around each edge. All vertices are ideal, with infinitely many tetrahedra existing around each vertex in a triangular tiling vertex figure. 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. Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space. (en)
  • 在幾何學中，六階四面體堆砌是一種由四面體完全填滿仿緊雙曲空間的幾何結構，屬於正圖形，每條邊都是6個四面體的公共邊，其所有頂點都是無窮遠點，每個頂點都是無窮多個四面體的公共頂點，為正三角形鑲嵌的。其對偶幾何圖形為三階六邊形鑲嵌蜂巢體。 (zh)
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  • 在幾何學中，六階四面體堆砌是一種由四面體完全填滿仿緊雙曲空間的幾何結構，屬於正圖形，每條邊都是6個四面體的公共邊，其所有頂點都是無窮遠點，每個頂點都是無窮多個四面體的公共頂點，為正三角形鑲嵌的。其對偶幾何圖形為三階六邊形鑲嵌蜂巢體。 (zh)
  • In hyperbolic 3-space, the order-6 tetrahedral honeycomb is a paracompact regular space-filling tessellation (or honeycomb). It is paracompact because it has vertex figures composed of an infinite number of faces, and has all vertices as ideal points at infinity. With Schläfli symbol {3,3,6}, the order-6 tetrahedral honeycomb has six ideal tetrahedra around each edge. All vertices are ideal, with infinitely many tetrahedra existing around each vertex in a triangular tiling vertex figure. (en)
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  • Order-6 tetrahedral honeycomb (en)
  • 六階四面體堆砌 (zh)
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