In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane.
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).
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.
This hyperbolic geometry-related article is a stub.