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In the geometry of hyperbolic 3-space, the order-7 hexagonal tiling honeycomb a regular space-filling tessellation (or honeycomb) with Schläfli symbol {6,3,7}.
Contents
Geometry
All vertices are ultra-ideal (existing beyond the ideal boundary) with seven hexagonal tilings existing around each edge and with an order-7 triangular tiling vertex figure.
Closeup
Related polytopes and honeycombs
It a part of a sequence of regular polychora and honeycombs with hexagonal tiling cells.
Infinite-order hexagonal tiling honeycomb
In the geometry of hyperbolic 3-space, the infinite-order hexagonal tiling honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {6,3,∞}. It has infinitely many hexagonal tiling {6,3} around each edge. All vertices are ultra-ideal (Existing beyond the ideal boundary) with infinitely many hexagonal tilings existing around each vertex in an infinite-order triangular tiling vertex arrangement.
Symmetry constructions
It has a second construction as a uniform honeycomb, Schläfli symbol {6,(3,∞,3)}, Coxeter diagram, , with alternating types or colors of hexagonal tiling cells.