, Volume 59, Issue 1-2, pp 55-73

Regular projective polyhedra with planar faces I

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This is the first of two papers in which we classify the regular projective polyhedra in \( \Bbb P^3 \) 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.

Received: February 6, 1998; revised version: December 10, 1998.