Surfaces and tiled surfaces
| (2,4,5)- tiling of the hyperbolic plane
| (2,5,5)- tiling of the hyperbolic plane
| (3,5,5)- tiling of the hyperbolic plane
| (4,3,3)- tiling of the hyperbolic plane
A tiling is divisible if it can be divided into a finer kaleidoscopic tiling.
An example is the tiling of the torus by rectangles which is refined by
the tiling by (2,4,4) triangles, pictured below. Each divisible tiling
of a surface comes from a divisible tiling of the hyperbolic plane. All
such tilings have been classified . There are four types of tilings. The
description and links to the tables and pictures are below:
Eight cases of tilings of triangles. There are six infinite families and
two exceptional cases.
Thirty four cases tilings of quadrilaterals by triangles with free vertices.
Because there are free vertices each one gives rise to infinite family
of divisible tilings.
Twenty seven tilings of quadrilaterals by triangles without free vertices.
There are no families.
Two tilings of quadrilaterals by quadrilaterals.
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Last modified April 4, 2001