Exploration. Illustration. Discussion.

The purpose of this site is to catalog, illustrate and discuss results and ideas related to transpositional topologies. These highly symmetric and regular discrete surfaces are based on combinatorial prototiles and simple, generative rules, that grow the surfaces tile by tile.

Look for the same prototile repeating itself, while browsing the finite and infinite surfaces under tilegraphs.

For more on how colour begets shape and some hopefully illuminating illustrations see Glueing & Looping in the Framework section. For a more formal introduction, see our paper posted here.

If you have comments, questions or would be interested in exchanging ideas please contact us.