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|120px |120px |- align=center |120px |120px |120px |120px |- align=center |120px |120px |120px |} In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells. In 3-dimensional hyperbolic space there are 23 Coxeter group families of paracompact uniform honeycombs, generated as Wythoff constructions, and represented by ring permutations of the Coxeter diagrams for each family. These families can produce uniform honeycombs with infinite or unbounded facets or vertex figure, including ideal vertices at infinity, similar to the hyperbolic uniform tilings in 2-dimensions. == Regular paracompact honeycombs == Of the uniform paracompact H3 honeycombs, 11 are regular, meaning that their group of symmetries acts transitively on their flags. These have Schläfli symbol , , , , , , , , , , and , and are shown below. !Face type !Edge figure !Vertex figure !Dual !Coxeter group |- BGCOLOR="#ffe0e0" align=center |Order-6 tetrahedral honeycomb||||||||||||||||rowspan=2|() |- BGCOLOR="#e0e0ff" align=center |Hexagonal tiling honeycomb|||||||||||||| |- BGCOLOR="#ffe0e0" align=center |Order-4 octahedral honeycomb||||||||||||||||rowspan=2|() |- BGCOLOR="#e0e0ff" align=center |Square tiling honeycomb|||||||||||||| |- BGCOLOR="#e0e0e0" align=center |Triangular tiling honeycomb||||||||||||||Self-dual||() |- BGCOLOR="#ffe0e0" align=center |Order-6 cubic honeycomb||||||||||||||||rowspan=2|() |- BGCOLOR="#e0e0ff" align=center |Order-4 hexagonal tiling honeycomb|||||||||||||| |- BGCOLOR="#e0e0e0" align=center |Order-4 square tiling honeycomb||||||||||||||Self-dual||() |- BGCOLOR="#ffe0e0" align=center |Order-6 dodecahedral honeycomb||||||||||||||||rowspan=2|() |- BGCOLOR="#e0e0ff" align=center |Order-5 hexagonal tiling honeycomb|||||||||||||| |- BGCOLOR="#e0e0e0" align=center |Order-6 hexagonal tiling honeycomb||||||||||||||Self-dual||() |} 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Paracompact uniform honeycombs」の詳細全文を読む スポンサード リンク
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