Archimedean
This project displays views of the Archimedean solids and their duals.
The Archimedean solids are the 13 polyhedra whose symmetry group act transitively on vertices, barring the Platonic solids and some trivial examples such as prism and antiprisms. This means that every vertex "looks the same" and there are rotations mapping the polyhedron to itself and mapping any vertex to any other. As a result, the faces of the Archimedean solids are all regular polygons.
The dual of a polyhedron is the polyhedron obtained by replacing every vertex by a face and every face by a vertex. As every vertex are isomorphic in an Archimedean solid, their duals have the property that all of their faces are isomorphic as well, although the are not regular polygons.
Triakis tetrahedron (dual of the truncated tetrahedron)
Rhombic dodecahedron (dual to the cuboctahedron)
Triakis octahedron (dual to the truncated cube)
Tetrakis hexahedron (dual to the truncated octahedron)
Deltoidal icositetrahedron (dual to the Rhombicuboctahedron)
Disdyakis dodecahedron (dual to the truncated cubocahedron)
Pentagonal icositetrahedron (dual to the snub cube)
Rhombic triacontahedron (dual to the icosidodecahedron)
Triakis icosahedron (dual to the truncated dodecahedron)
Pentakis dodecahedron (dual to the truncated icosahedron)
Deltoidal hexecontahedron (dual to the rhombicosidodecahedron)
Disdyakis triacontahedron (dual to the truncated icosidodecahedron)
Pentagonal hexecontahedron (dual to the snub dodecahedron)
Stereographic images: look at the left picture with your right eye and vice versa to see the images in three-dimensions.
The Archimedean solids
The Catalan solids
