The tetrahedron has another interesting and unique property: its dual is also the tetrahedron. We get a shape's dual by switching faces for corners and vice versa, while keeping the number of edges unchanged. The cube and octahedron are duals, as are the cuboctahedron and rhombic dodecahedron.

The dual of a shape need not be any specific size, however we may specify that the edges of the two shapes intersect at right angles. By combining duals in this way, we define the vertices of additional shapes.