Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Convex polytopes with convex nets

G. C. Shepharda1

a1 University of East Anglia, Norwich NR4 7TJ, England

The idea of a net will be familiar to anyone who has made a model of a three-dimensional convex polytope (3-polytope) out of a flat sheet of card or similar material. To begin with, one cuts out a polygon, and then the model is formed by folding this and joining its edges in an appropriate manner. For example, Fig. 1 illustrates two nets for a regular tetrahedron. The folds are indicated by broken lines and lettering (either of the edges or of the vertices) indicates how the edges are to be joined.

(Received February 10 1975)