# How to turn a tetrahedron into a cube and similar transformations

### G.C. Shephard

East Anglia University, Norwich, UK

## Abstract

Suppose that the surface of a polyhedron $P_{1}$ is cut in such a way that it can be opened out flat to form a connected region $R$ in the plane and that $R$, by introducing suitable folds, can be made into the net of a polyhedron $P_{2}$. Then we write $P_{1} \Rightarrow P_{2}$ and say that $P_{1}$ is *transformed* into $P_{2}$. In this paper we give many examples of the transformation of polyhedra and investigate the properties of the relation $\Rightarrow$ .

## Cite this article

G.C. Shephard, How to turn a tetrahedron into a cube and similar transformations. Enseign. Math. 59 (2013), no. 1/2, pp. 115–131

DOI 10.4171/LEM/59-1-4