One of these solids, the truncated tetrahedron, can be inscribed in a regular tetrahedron. The next six can be inscribed in either a cube or an octahedron, and the last six in either a dodecahedron or an icosahedron. The 'truncated' solids are so called because each can be constructed by cutting off the corners of some other solid, but the truncated cuboctahedron and icosidodecahedron require a distortion in addition to convert rectangles into squares. So the better names for these two solids are 'Great Rhombicuboctahedron' and 'Great Rhombicosidodecahedron'. The syllable 'rhomb-' shows that one set of faces lies in the planes of the rhombic dodecahedron and rhombic triacontahedron respectively.
All Archimedean solids are inscribable in a sphere.
F 4 a square. The number of V ertices and E dges are also given as coeficients e.g. a cube would have 8V and 12E References Adams, Mark S. Archimedean and Platonic Solids. S.J. HomePage with 13 parts, each with its own icon taken from the family of the 13 Achimedean semiregular polyhedra. S.J. They are the 13 Achimedean semiregular polyhedra.