Images
Surfaces and tiled surfaces
Hyperbolic tilings
(2,4,5) tiling of the hyperbolic plane 
T245.gif 

(2,5,5) tiling of the hyperbolic plane 
T255.gif 

(3,5,5) tiling of the hyperbolic plane 
T355.gif 

(4,3,3) tiling of the hyperbolic plane 
T433.gif 

Divisible tilings
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.
Home
 Contributors
 Publications
 Images  Archives
 Links
Send questions and comments to: allen.broughton@rosehulman.edu
Last modified April 4, 2001
