Description of the ninety two RFP and their derivation from the simple ones

Abstract

In this chapter, we give a complete list and a systematic classification of all the convex RFP. For this purpose, we need to use the notion of a simple (elementary) RFP (see definition 13 of chapter 2). Thus, for example, the prisms P₃, P₄, P₅,… are all simple; so are the antiprisms A₄, A₅, A₆, …, however, A₃, the octahedron, is not simple since it can be decomposed into two square pyramids (figure 12.1); nor is the icosahedron, since any pentagonal pyramid may be separated from the main body and both parts are RFP. Indeed, the icosahedron gives rise to five further RFP shown in figure 12.2.