A Polyhedron is a shape, made up of faces. 'Poly-' is from the Greek word for 'many' and '-hedron' is a Greek combining form meaning 'base', 'seat', or 'face'. |

Vertices Edges Faces Edges/Face? Edges/Vertex? Symmetry group Tetrahedron 4 6 4 3 3 Td Cube 8 12 6 4 3 Oh Octahedron 6 12 8 3 4 Oh Dodecahedron 20 32 12 5 3 Ih Icosahedron 12 32 20 3 5 Ih |

Vertices Edges Faces Edges/Face Edges/Vertex Symmetry group Tetrahedron 4 6 4 3 3 Td Cube 8 12 6 4 3 Oh Octahedron 6 12 8 3 4 Oh Dodecahedron 20 32 12 5 3 Ih Icosahedron 12 32 20 3 5 Ih |

Polyhedra which are vertex- and edge-uniform, but not necessarily face-uniform, are called quasi-regular and include two more convex forms (the cuboctahedron and icosidodecahedron, as well as a few non-convex forms. The duals of these are the edge- and face-uniform polyhedra: the [rhombic dodecahedron]?, [rhombic triacontahedron]?, plus whatever the non-convex ones are. |

Polyhedra which are vertex- and edge-uniform, but not necessarily face-uniform, are called quasi-regular and include two more convex forms (the cuboctahedron and icosidodecahedron, as well as a few non-convex forms. The duals of these are the edge- and face-uniform polyhedra: the [rhombic dodecahedron]?, [rhombic triacontahedron]?, plus whatever the non-convex ones are. No other convex edge-uniform polyhedra exist. |

/Talk? |