The 13 duals of the archimedean polyhedra
The 13 duals of the archimedean polyhedra and their nets. These polyhedra have equal faces and regular vertex figures; the faces can be also non-regular polygons and the vertex figures are not necessarily alike. Moreover, the group of symmetry is transitive on the faces (if we take any couple of faces, there's a symmetry of the polyhedron that maps the first face into the second one), so they could be used as impartial dice. The polyhedra with these properties are the 13 polyhedra in the figure and the polyhedra belonging to two infinite families: the bipyramids and the trapezohedra, that can be as well shapes for impartial dice.
This image is taken from M. Dedò's "Forme", ed. Decibel-Zanichelli, 1999.
© matematita
The image belongs to the sections...:
Uniform polyhedra and their duals (3D geometry)
