Abstract: The invention provides a basic building piece capable of combining with other, identical basic building pieces to form three-dimensional geometric models of the five regular polyhedrons (tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron), or more accurately, the Archimedean counterparts or truncated versions of these polyhedrons, as well as structures based on combinations of these solids, and other irregular and complex solids and shells. The basic building piece comprises a flat, generally hexagonal member carrying three types of fastening devices on its edges and surfaces to enable the desired variety of connection configurations with other, identical building pieces, and the structures resulting therefrom. In one embodiment, completed forms utilize the interplay of transparent colored pieces to create aesthetic patterns and multicolor relationships.