The great majority of polyhedra can either be discovered from the honeycombs or by combining other polyhedra.
The honeycombs do not always immediately give polyhedra. Many more can be discovered by taking the arrangement of vertices around the vertex of a honeycomb and then seeing what other polyhedra can be created from this.
Many polyhedra can be discovered simply by plugging the simpler polyhedra together, either directly or indirectly with connectors (usually octahedra, prisms or pairs of triangular prisms). The slabs are obtained by connecting pairs of tilings with tubes, either cubes, octahedra or prisms. Slabs themselves be further connected together. Layered polyhedra are obtained by connecting tilings and deformed tilings with a variety of tubes and connectors.
The polyhedra of the following pages cannot be discovered by the above methods, and this makes them interesting. Almost all of these are new discoveries.
Another way that polyhedra can be discovered is by face splitting, for example a square face can be split into two triangular faces. If the square faces of a cuboctahedron are replaced by pairs of triangles, then a snub cuboctahedron is obtained. Many, but not all, of these unstructured polyhedra can be discovered in this way.