Centrally symmetric convex polyhedra with regular polygonal faces.

First we prove that the class CI of centrally symmetric convex polyhedra with regular polygonal faces consists of 4 of the 5 Platonic, 9 of the 13 Archimedean, 13 of the 92 Johnson solids and two infinite families of 2n-prisms and (2n + 1)-antiprisms. Then we show how the presented maps of their halves (obtained by identification of all pairs of antipodal points) in the projective plane can be used for obtaining their ag graphs and symmetry-type graphs. Finally, we study some linear dependence relations between polyhedra of the class CI. [ABSTRACT FROM AUTHOR]