The great dodecahedron is formed from twelve intersecting pentagons and the great icosahedron by twenty intersecting triangles. These have sides made up of regular polygons and vertices which are all the same but they are made of more than one type of polygon. There are thirteen of these and they are known as the Archimedean polyhedra because they were first enumerated by Archimedes. Polygons produced in this way are known as non-convex or stellated polygons and can be used to generate many beautiful polyhedra. The two stellated dodecahedra mentioned above are examples which also happen to be regular because they are made of one type of polygon.
Every polyhedron has a dual polyhedron where each vertex corresponds to a plane and vice versa.
Two or more polyhedra of the same types can be interpenetrated to form another series of attractive solids. A brief summary of the techniques that I used to make the models shown here is given below. The polygons required to produce the model are first drawn on paper. The actual shapes needed will depend on the polyhedron being made. Initially all the shapes were drawn by hand using a drawing board, compass, ruler etc.