Families of polyhedra

In the upper part of Figure 1(a) we show the net N(P) of a polyhedron P . If this is cut out of paper, folded along the (dashed and solid) lines, and edges with the same labels (a, b, c, . . . ) joined together, we obtain a model of the surface S(P) of a polyhedron P . Here P is a 4-spindle (a cube with two 4-pyramids adjoined to opposite faces). If, instead of assembling S(P) as described above, we cut the net into two pieces along the solid line we get the regions shown in the lower part of Figure 1(a). These are the nets of two polyhedra P1 and P2. P1, on the left of the diagram, is a 3-prism with a tetrahedron adjoined to one of its triangular faces (known as an elongated tetrahedron), and P2, on the right, is a 4-pyramid. Since P1 and P2 were derived from P , borrowing biological terminology, we shall say that P is a parent and P1 and P2 are its offspring. We write