Ceramic orthogonal polyhedra

David Richter, a mathematician at the University of Western Michigan, recently found himself with a surfeit of ceramic orthogonal polyhedra and, knowing of my own interest in orthogonal polyhedra, generously offloaded two of them to me. They fit nicely in my office together with the paper and crochet orthogonal polyhedra I already had: The blue one is an orthogonal realization of Boy’s surface, an immersion of the projective plane into three-dimensional space with three-way symmetry and a single triple crossing point. The idea to make an orthogonal version comes from Jean Pierre Petit’s Le Topologicon, where its relation to the usual curved version can maybe be seen more clearly than in my photographs. The model hides a hidden graph embedding: the uncolored edges form the boundaries of a hemi-dodecahedron, an embedding of the Petersen graph with six pentagonal faces, each adjacent to all five others. The other ceramic model, colored yellow, green, and red, is an orthogonal realization…