The Kepler-Poinsot polyhedra are also known as the regular star polyhedra. Each one of these shapes has faces which are congruent regular convex polygons or star polygons and has the same number of faces meeting at each vertex.
Challenge your students by having them construct two of these 3D models; the great dodecahedron, and the great icosahedron. Each model comes in two forms. Black and white so that students can decorate them, and colored versions, so that they may come to visualize, and discover special relationships between the sides, edges, and vertices.