## Quick Reference

A convex polyhedron is regular if all its faces are alike and all its vertices are alike. More precisely, this means that*p* of edges, and*q* of edges meet at each vertex. Notice that the polyhedron shown here, with 6 triangular faces, satisfies (i), but is not regular because it does not satisfy (ii). There are five regular convex polyhedra, known as the Platonic solids:*p*=3, *q*=3),*p*=4, *q*=3),*p*=3, *q*=4),*p*=5, *q*=3),*p*=3, *q*=5).

*p* of edges, and

*q* of edges meet at each vertex.

*p*=3, *q*=3),

*p*=4, *q*=3),

*p*=3, *q*=4),

*p*=5, *q*=3),

*p*=3, *q*=5).

Plane of symmetry.

*Subjects:*
Mathematics.

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