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  "body": "\n## Description\n\nAn *Archimedean solid* is a convex [[polyhedron|0325SGSJAR]] with two properties.\nIts faces are [[regular polygons|01KJJ9A400]] of at least two different kinds.\nIts [[symmetry group|0ZG3Z5JZ85]] acts transitively on its vertices.\nThe prisms and antiprisms also have these properties and are excluded.\nUp to similarity there are thirteen Archimedean solids.\nSeven have the symmetry of the tetrahedron or the cube: the truncated tetrahedron, cuboctahedron, truncated cube, truncated octahedron, rhombicuboctahedron, truncated cuboctahedron and snub cube.\nSix have the symmetry of the icosahedron: the icosidodecahedron, truncated dodecahedron, truncated icosahedron, rhombicosidodecahedron, truncated icosidodecahedron and snub dodecahedron.\n\n## Remarks\n\nThe truncated tetrahedron has $4$ triangles and $4$ hexagons as faces, $12$ vertices and $18$ edges.\n[[Euler's polyhedron formula|09HT3P35YP]] checks out: $12 - 18 + 8 = 2$.\nThe truncated icosahedron, the pattern of a classic football, has $12$ pentagons, $20$ hexagons, $60$ vertices and $90$ edges, and $60 - 90 + 32 = 2$.\nThe snub cube and the snub dodecahedron come in two mirror image forms, and some authors count these separately.\nAsking only that all vertices look alike locally is weaker: the elongated square gyrobicupola satisfies that condition but is not vertex-transitive.\nThe [[Platonic solids|017E5PRS1Q]] are the vertex-transitive convex polyhedra with a single kind of regular face.\n\n## Explanations\n\n### L1 human\n\nThe Archimedean solids are the next most regular solids after the five Platonic solids.\nTheir faces are regular polygons of more than one shape, such as triangles and squares.\nEvery corner looks exactly like every other corner, and a rotation or reflection of the solid can move any corner to any other.\n",
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