Regular projective polyhedra with planar faces I

Abstract

This is the first of two papers in which we classify the regular projective polyhedra in ℙ3 with planar faces. Here, we develop the basic notions; we introduce a new diophantine trigonometric equation, which plays a key role in the classification theorem, relating the combinatorial and geometric parameters of such polyhedra, and conclude with the case in which the polyhedron is an embedded surface. © Birkhäuser Verlag, Basel, 2000.