In geometry an Archimedean solid is a highly symmetric, semiregular 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.
The symmetry of the Archimedean solids excludes the members of the dihedral group, the prisms and antiprisms. The Archimedean solids can all be made via Wythoff constructions from the Platonic solids with tetrahedral, octahedral and icosahedral symmetry.
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The Archimedean solids take their name from Archimedes, who discussed them in a nowlost work. During the Renaissance, artists and mathematicians valued pure forms and rediscovered all of these forms. This search was completed around 1620 by Johannes Kepler, who defined prisms, antiprisms, and the nonconvex solids known as the KeplerPoinsot polyhedra.
There are 13 Archimedean solids (15 if the mirror images of two enantiomorphs, see below, are counted separately).
Here the vertex configuration refers to the type of regular polygons that meet at any given vertex. For example, a vertex configuration of (4,6,8) means that a square, hexagon, and octagon meet at a vertex (with the order taken to be clockwise around the vertex).
Name (Vertex configuration) 
Transparent  Solid  Net  Faces  Edges  Vertices  Symmetry group  

truncated tetrahedron (3.6.6) 
(Animation) 
8  4 triangles 4 hexagons 
18  12  T_{d}  
cuboctahedron (3.4.3.4) 
(Animation) 
14  8 triangles 6 squares 
24  12  O_{h}  
truncated cube or truncated hexahedron (3.8.8) 
(Animation) 
14  8 triangles 6 octagons 
36  24  O_{h}  
truncated octahedron (4.6.6) 
(Animation) 
14  6 squares 8 hexagons 
36  24  O_{h}  
rhombicuboctahedron or small rhombicuboctahedron (3.4.4.4 ) 
(Animation) 
26  8 triangles 18 squares 
48  24  O_{h}  
truncated cuboctahedron or great rhombicuboctahedron (4.6.8) 
(Animation) 
26  12 squares 8 hexagons 6 octagons 
72  48  O_{h}  
snub cube or snub hexahedron or snub cuboctahedron (2 chiral forms) (3.3.3.3.4) 
(Animation) (Animation) 
38  32 triangles 6 squares 
60  24  O  
icosidodecahedron (3.5.3.5) 
(Animation) 
32  20 triangles 12 pentagons 
60  30  I_{h}  
truncated dodecahedron (3.10.10) 
(Animation) 
32  20 triangles 12 decagons 
90  60  I_{h}  
truncated icosahedron or buckyball or football/soccer ball (5.6.6 ) 
(Animation) 
32  12 pentagons 20 hexagons 
90  60  I_{h}  
rhombicosidodecahedron or small rhombicosidodecahedron (3.4.5.4) 
(Animation) 
62  20 triangles 30 squares 12 pentagons 
120  60  I_{h}  
truncated icosidodecahedron or great rhombicosidodecahedron (4.6.10) 
(Animation) 
62  30 squares 20 hexagons 12 decagons 
180  120  I_{h}  
snub dodecahedron or snub icosidodecahedron (2 chiral forms) (3.3.3.3.5) 
(Animation) (Animation) 
92  80 triangles 12 pentagons 
150  60  I 
The number of vertices is 720° divided by the vertex angle defect.
The cuboctahedron and icosidodecahedron are edgeuniform and are called quasiregular.
The duals of the Archimedean solids are called the Catalan solids. Together with the bipyramids and trapezohedra, these are the faceuniform solids with regular vertices.
The snub cube and snub dodecahedron are known as chiral, as they come in a lefthanded (Latin: levomorph or laevomorph) form and righthanded (Latin: dextromorph) form. When something comes in multiple forms which are each other's threedimensional mirror image, these forms may be called enantiomorphs. (This nomenclature is also used for the forms of certain chemical compounds).
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From Archimedes Greek mathematician and engineer
Singular 
Plural 
Archimedean solid (plural Archimedean solids)


