Archimedean solid
From The Art and Popular Culture Encyclopedia
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In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices. They are distinct from the Platonic solids, which are composed of only one type of polygon meeting in identical vertices, and from the Johnson solids, whose regular polygonal faces do not meet in identical vertices.
"Identical vertices" are usually taken to mean that for any two vertices, there must be an isometry of the entire solid that takes one vertex to the other. Sometimes it is instead only required that the faces that meet at one vertex are related isometrically to the faces that meet at the other. This difference in definitions controls whether the pseudorhombicuboctahedron is considered an Archimedean solid or a Johnson solid.
Prisms and antiprisms, whose symmetry groups are the dihedral groups, are generally not considered to be Archimedean solids, despite meeting the above definition. With this restriction, there are only finitely many Archimedean solids. They can all be made via Wythoff constructions from the Platonic solids with tetrahedral, octahedral and icosahedral symmetry.
See also
- Aperiodic tiling
- Catalan solid
- List of uniform polyhedra
- Platonic solid
- Johnson solid
- Toroidal polyhedron
- Quasicrystal
- semiregular polyhedron
- regular polyhedron
- uniform polyhedron
