Order-4 heptagonal tiling
In geometry, the order-4 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of.
Symmetry
This tiling represents a hyperbolic kaleidoscope of 7 mirrors meeting as edges of a regular heptagon. This symmetry by orbifold notation is called *2222222 with 7 order-2 mirror intersections. In Coxeter notation can be represented as, removing two of three mirrors in the symmetry.The kaleidoscopic domains can be seen as bicolored heptagons, representing mirror images of the fundamental domain. This coloring represents the uniform tiling t1 and as a quasiregular tiling is called a heptaheptagonal tiling.
Related polyhedra and tiling
This tiling is topologically related as a part of sequence of regular tilings with heptagonal faces, starting with the heptagonal tiling, with Schläfli symbol, and Coxeter diagram, progressing to infinity.[Heptagonal tiling|] | Order-7 [heptagonal tiling|] |
This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with four faces per vertex, starting with the octahedron, with Schläfli symbol, and Coxeter diagram, with n progressing to infinity.