Tiling a Hyperbolic Pair of Pants
Proceedings of Bridges 2025: Mathematics and the Arts
Pages 177–182
Regular Papers
Abstract
A hyperbolic regular octagon with 45° interior angles can be edge-identified to construct a double torus, analogous to how a square can be edge-identified to form a torus. A pair of pants arises as an intermediate step in this process, much like how a cylinder appears as an intermediate step when constructing a torus. In this paper we show how to build a regular octagon with 45° interiors angles using the hyperbolic (6,6,8)tiling. The final model is made of EVA foam pieces which allow easily constructing a pair of pants from the octagon.