A Woven Klein Quartic

Curvature is determined by local geometry, and this can be controlled. A pattern with a particular symmetry is often in an infinite family of patterns, all with the same underlying motif, but of varied curvature

Orbifold Geometrization

I was curious about the actual algorithm for geometrizing an orbifold — it’s only lightly sketched at in Thurston’s Three Dimensional Topology and Geometry. Hence the app. The details are now inside some javascript: Check


Welcome to hyperbolic geometry, with this beautiful steel rendition of the 5444 tiling: at each corner three squares and one pentagon meet, forcing the surface to bend and coil up with negative curvature. The straight


Foam fragments of the hyperbolic plane, formed from straight flat strips of foam. Differently spaced teeth on the sides of the strips force them to curve at a steady rate: any surface with equally spaced