Bridges 2010 Short Paper

Models of Locally Regular Heptagonal Dodecahedra
David I. McCooey
(Proceedings pages 479–482)


We present models of polyhedra built from 12 heptagons meeting three per vertex. Unlike the analogous case with 12 pentagons, where there is a single unique combinatorial structure, there are six combinatorially distinct ways to combine 12 heptagons, meeting three per vertex, into a (possibly self-intersecting) polyhedron. We identified realizable (non-self-intersecting) examples for five of the six possible structures, and fabricated physical models of them. They all necessarily have genus 2 (topologically equivalent to a 2-holed donut), and they appear in a variety of aesthetically pleasing symmetries. These models demonstrate a form of art emerging from mathematics.