Images
Surfaces and tiled surfaces
Hyperbolic tilings
| (2,4,5)- tiling of the hyperbolic plane |
T245.gif |
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| (2,5,5)- tiling of the hyperbolic plane |
T255.gif |
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| (3,5,5)- tiling of the hyperbolic plane |
T355.gif |
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| (4,3,3)- tiling of the hyperbolic plane |
T433.gif |
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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:
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Eight cases of tilings of triangles. There are six infinite families and
two exceptional cases.
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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.
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Twenty seven tilings of quadrilaterals by triangles without free vertices.
There are no families.
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Two tilings of quadrilaterals by quadrilaterals.
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Send questions and comments to: allen.broughton@rose-hulman.edu
Last modified April 4, 2001
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