An **Archimedean** solid is a semi-regular (ie vertex-uniform, but not face-uniform) convex polyhedron with regular polygons for faces. Compare to Platonic solids, which are face-uniform, and Johnson solids, which need not be vertex-uniform. The prisms and antiprisms, though they meet the above criteria, are typically excluded from the Archimedean solids because they do not have a higher polyhedral symmetry.

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These solids were known to be discussed by Archimedes, although the complete record is lost. During the Renaissance, artists and mathematicians valued *pure forms* and rediscovered all of these forms. This search culminated in the work of Johannes Kepler circa 1619, who defined prisms, antiprisms, and the non-convex solids known as Kepler solids.

There are thirteen Archimedean solids, (ignoring that two are enantiomorphs).

- cuboctahedron (with a triangle, a square, a triangle, and a square in sequence at each vertex)
- icosidodecahedron (with a triangle, a pentagon, a triangle, and a pentagon in sequence at each vertex)
- [truncated tetrahedron]? (with a triangle, a hexagon, and a hexagon in sequence at each vertex)
- [truncated octahedron]? (with a square, a hexagon, and a hexagon in sequence at each vertex)
- [truncated cube]? (with a triangle, an octagon, and an octagon in sequence at each vertex)
- truncated icosahedron (with a pentagon, a hexagon,and a hexagon in sequence at each vertex)
- [truncated dodecahedron]? (with a triangle, a degagon, and a degagon in sequence at each vertex)
- rhombicuboctahedron, also named the small rhombicuboctahedron (with a triangle, a square, a square, and a square in sequence at each vertex)
- [truncated cuboctahedron]?, also named the great rhombicuboctahedron (with a square, a hexagon, and an octagon in sequence at each vertex)
- rhombicosidodecahedron?, also named the small rhombicosidodecahedron (with a triangle, a square, a pentagon, and a square in sequence at each vertex)
- [truncated icosidodecahedron]?, also named the great rhombicosidodecahedron (with a square, a hexagon, and a degagon in sequence at each vertex)
- [snub cube]?, also named the snub cuboctahedron (with a triangle, a triangle, a triangle, a triangle, and a square in sequence at each vertex)
- [snub dodecahedron]?, also named the snub icosidodecahedron (with a triangle, a triangle, a triangle, a triangle, and a pentagon in sequence at each vertex)

As a reminder, a triangle has three sides, a square has four sides, a pentagon has five sides, a hexagon has six sides, an octagon has eight sides, and a degagon has ten sides. The first two solids (cuboctahedron and icosidodecahedron) are edge-uniform and are called quasi-regular.

The last two (snub cube and snub dodecahedron) are known as *chiral*, as they come in a left-handed (latin: levomorph or laevomorph) form and right-handed (latin: dextromorph) form. When something comes in multiple forms based on rotation, these forms may be called enantiomorphs. (This nomeclature is also used for the forms of [chemical compounds]?). These forms are similar to reflections in a mirror, but are actual three-dimensional shapes.

The duals of the Archimedean solids are called the [Catalan solids]?. Together with the bipyramids and trapezohedra?, these are the face-uniform solids with regular vertices.

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