Archimedean Solid - Classification

Classification

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 Point group
truncated tetrahedron
(3.6.6)
8 4 triangles
4 hexagons		 18 12 Td
cuboctahedron
(3.4.3.4)
14 8 triangles
6 squares		 24 12 Oh
truncated cube
or truncated hexahedron
(3.8.8)
14 8 triangles
6 octagons		 36 24 Oh
truncated octahedron
(4.6.6)

14 6 squares
8 hexagons		 36 24 Oh
rhombicuboctahedron
or small rhombicuboctahedron
(3.4.4.4 )
26 8 triangles
18 squares		 48 24 Oh
truncated cuboctahedron
or great rhombicuboctahedron
(4.6.8)
26 12 squares
8 hexagons
6 octagons		 72 48 Oh
snub cube
or snub hexahedron
or snub cuboctahedron
(2 chiral forms)
(3.3.3.3.4)


38 32 triangles
6 squares		 60 24 O
icosidodecahedron
(3.5.3.5)
32 20 triangles
12 pentagons		 60 30 Ih
truncated dodecahedron
(3.10.10)
32 20 triangles
12 decagons		 90 60 Ih
Truncated icosahedron
(5.6.6 )
32 12 pentagons
20 hexagons		 90 60 Ih
rhombicosidodecahedron
or small rhombicosidodecahedron
(3.4.5.4)
62 20 triangles
30 squares
12 pentagons		 120 60 Ih
truncated icosidodecahedron
or great rhombicosidodecahedron
(4.6.10)
62 30 squares
20 hexagons
12 decagons		 180 120 Ih
snub dodecahedron
or snub icosidodecahedron
(2 chiral forms)
(3.3.3.3.5)


92 80 triangles
12 pentagons		 150 60 I

Some definitions of semiregular polyhedron include one more figure, the elongated square gyrobicupola or "pseudo-rhombicuboctahedron".

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