The Stellated Archimedeans
The class of semi-regular non-convex or star polyhedra, which are not prisms nor anti-prisms. This set bears the same relationship to the archimedean solids as the kepler-poinsot star polyhedra do to the platonic solids. The exact size of the set depends on the precise restrictions made. For example, some potential polyhedra have plane faces passing through their centre, faces with both sides visible on the outside, or faces which share the same plane. Here, we will reject such shapes.
The stellated archimedians fall in to three subsets, based on the symmetry they possess.
- Those with the symmetry of the cube and octahedron:
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Those which have the symmetry of the icosahedron
and dodecahedron.
- Small Ditrigonal Icosidodecahedron
- Small Icosicosidodecahedron
- Dodecadodecahedron
- Truncated Great Dodecahedron
- Rhombidodecadodecahedron*
- Great Ditrigonal Dodecicosidodecahedron
- Icosidodecatruncated Icosidodecahedron
- Great Ditrigonal Icosidodecahedron
- Great Icosidodecahedron
- Truncated Great Icosahedron
- Quasitruncated Small Stellated Dodecahedron
- Great Dodecicosidodecahedron
- Quasitruncated Great Stellated Dodecahedron
- Great Quasitruncated Icosidodecahedron*
- Those which have the symmetry of the snub dodecahedron: