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Order-6 tetrahedral honeycomb : ウィキペディア英語版 | Order-6 tetrahedral honeycomb
|- |bgcolor=#e7dcc3|Coxeter diagrams|| ↔ |- |bgcolor=#e7dcc3|Cells|| 40px |- |bgcolor=#e7dcc3|Faces||Triangle |- |bgcolor=#e7dcc3|Edge figure||Hexagon |- |bgcolor=#e7dcc3|Vertex figure||Triangular tiling 80px 80px |- |bgcolor=#e7dcc3|Dual||Hexagonal tiling honeycomb, |- |bgcolor=#e7dcc3|Coxeter groups||, |- |bgcolor=#e7dcc3|Properties||Regular, quasiregular |} In the geometry of hyperbolic 3-space, the order-6 tetrahedral honeycomb a paracompact regular space-filling tessellation (or honeycomb). It is called ''paracompact'' because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol . It has six tetrahedra around each edge. All vertices are ideal vertices with infinitely many tetrahedra existing around each ideal vertex in an triangular tiling vertex arrangement.〔Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III〕 == Symmetry constructions ==
It has a second construction as a uniform honeycomb, Schläfli symbol , with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is () ↔ () or : ↔ .
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