Truncated infinite-order triangular tiling

In geometry, the truncated infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{3,∞}.

Symmetry

The dual of this tiling represents the fundamental domains of *∞33 symmetry. There are no mirror removal subgroups of [(∞,3,3)], but this symmetry group can be doubled to ∞32 symmetry by adding a mirror. + Small index subgroups of [(∞,3,3)], (*∞33)TypeReflectional RotationalIndex12DiagramCoxeter(orbifold)[(∞,3,3)](*∞33)[(∞,3,3)]+(∞33)

Related polyhedra and tiling

This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (6.n.n), and [n,3] Coxeter group symmetry.

See also

List of uniform planar tilings Tilings of regular polygons Uniform tilings in hyperbolic plane

References

John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)

External links