Here are some of the hyperbolic and spherical tilings I created while working on my hyperbolic maze demo. The images are rendered from PostScript files which I created using a program that I wrote. The reason I made these was so that I could get comfortable with hyperbolic space. | |||

## Tiling #1Hyperbolic tiling with 7 equilateral triangles meeting at each vertex, Poincaré projection. Here the tiling is aligned to the center of one triangle. |
## Tiling #2Same as | ||

## Tiling #3Same as |
## Tiling #4Same as | ||

## Tiling #5Same as |
## Tiling #6This is seven equilateral triangles which have been subdivided uniformly in hyperbolic space. You might think of this as portion of a "hyperbolic geodesic dome", as the construction is completely analogous. The projection is Poincaré. | ||

## Tiling #7Same as |
## Tiling #8Here is the same hyperbolic geodesic dome, but under Klein projection. | ||

## Tiling #97-triangle Poincaré tiling, but with thickened edges. |
## Tiling #10This is the hyperbolic equivalent of an icosidodecahedron. In this tiling, each vertex is surrounded by two 7-gons and two triangles. | ||

## Tiling #11Same as |
## Tiling #12This is supposed to be a hyperbolic tiling where each vertex is surrounded by a 7-gon and two hexagons. The hexagons, unfortunately, aren’t quite regular. (They can be made regular by enlarging the 7-gons slightly.) | ||

## Tiling #13This is a spherical tiling of an icosahedron subdivided into a geodesic dome. The projection is stereographic and clamped to a radius of 5 units. | ## Tiling #14Same as | ||

## Tiling #15Same as |
## Tiling #16Same as |

This page © Bernie Freidin, 2000.

Last updated April 4th, 2000.