A dual of a polyhedron is made by placing a point in the centre of each face then joining these point to form another polyhedron inside the first. The diagram below shows an Icosahedron marked with yellow edges, a cross has been marked in the center of each face and lines drawn between to form a Dodecahedron inside the Icosahedron. The dodecahedron is the dual to the Icosahedron, if you repeat the process and join lines from the centre of the dodecahedron faces you will produce an Icosahedron inside the dodecahedron.