Classifying three-dimensional shapes

Reflective symmetry in three dimensions

Let me briefly look at reflective symmetry as it is applied to three-dimensional shapes. Two-dimensional shapes have reflective symmetry, with a line of symmetry dividing the shape into two matching halves, one a mirror image of the other. The same applies to three-dimensional shapes except that it is now a plane of symmetry that divides the shape into the two halves .

This is like taking a broad, flat knife and slicing right through the shape, producing two bits that are mirror images of each other. This cone, of course, has an infinite number of planes of symmetry, since any vertical slice through the apex of the cone can be used. All the three-dimensional shapes illustrated in the figures in this chapter have reflective symmetry. For example, the regular tetrahedron has six planes of symmetry. Children can experience this idea by slicing various fruits in half, or by using solid shapes made out of some moulding material.