A combinatorially regular dodecahedron of genus 3

AbstractWe give polyhedral realizations in E3 of two regular maps with automorphism group of order 192 by W. Dyck and F.A. Sherk. The polyhedra have self-intersections as the Kepler-Poinsot solids and maximal possible symmetry group. The polyhedral realization of Dyck's map is a dodecahedron built up of 12 octogons. Its visible part is a well-known object of delusion