In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}.
Constructions There are two uniform constructions of this tiling, first by the [7,4] kaleidoscope, and second by removing the last mirror, [7,4,1+], gives [7,7], (*772). + Two uniform constructions of 4.7.4.7NameTetraheptagonalTruncated heptaheptagonalImageSymmetry[7,4](*742)[7,7] = [7,4,1+](*772) = Symbolt{7,4}tr{7,7}Coxeter diagram
Symmetry There is only one simple subgroup [7,7]+, index 2, removing all the mirrors. This symmetry can be doubled to 742 symmetry by adding a bisecting mirror. + Small index subgroups of [7,7] TypeReflectionalRotationalIndex12DiagramCoxeter(orbifold)[7,7] = (*772)[7,7]+ = (772)
Related polyhedra and tiling
References John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
See also
Uniform tilings in hyperbolic plane List of regular polytopes
External links
Hyperbolic and Spherical Tiling Gallery KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings Hyperbolic Planar Tessellations, Don Hatch