How to describe or design a polyhedron (Q1842764)

The author discusses the following fundamental problems about spherical polyhedra in real 3-space. What data can be used to describe a polyhedron? And, for the design of the polyhedron, what independent choices can be made? The answers to these questions, if known, depend on the type of geometry (euclidean, similarity, projective, combinatorial) for which they are asked. The paper explores these problems in the context of some well-known classical results in geometry.