Abstract
For each odd prime p, there is a regular polyhedron Π p of type {3, p} with 1 2 ( p 2−1) vertices whose rotation group is PSL(2, p); its complete group is PSL(2, p) × Z 2 or PGL(2, p) as p ≡ 1 or 3 (mod 4). If p ≡ 1 (mod 4), then the group of Π p contains a central involution, and identification of antipodal vertices under this involution yields another regular polyhedron Π p 2 of type {3, p} with 1 4 ( p 2)−1) vertices and group PSL(2, p). Realizations of the polyhedra in euclidean spaces are briefly described.
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