Polyhedra  - Description and Animations

Platonic Solids

Types
 of
Faces
#
of
Edges
#
of
Vertices
       Tetrahedron4 triangles64
       Hexahedron6 squares128
       Octahedron88 triangles126
       Dodecahedron1212 pentagons3020
       Icosahedron2020 triangles3012

Archimedean Solids


       Truncated Tetrahedron84 triangles
6 hexagons
1812
       Cuboctahedron148 triangles
6 squares
2412
       Truncated Octahedron146 squares
8 hexagons
3624
       Truncated Hexahedron (Cube)148 triangles
6 octagons
3624
       Rhombicuboctahedron268 triangles
18 squares
4824
       Truncated cuboctahedron2612 squares
8 hexagons
6 octagons
7248
        Snub Cube, Left-Handed3832 triangles
6 squares
6024
        Snub Cube, Right-Handed3832 triangles
6 squares
6024
        Icosidodecahedron3220 triangles 12 pentagons6030
        Truncated Icosahedron
             (buckyball - soccerball)
3212 pentagons 20 hexagons9060
        Truncated Dodecahedron3220 triangles 12 decagons9060
        Rhombicosidocehedron6220 triangles 30 squares
12 pentagons
12060
        Truncated Icosidodecahedron6230 squares
20 hexagons 12 decagons
180120
        Snub Dodecahedron, Left-Handed9280 triangles 12 pentagons150150
        Snub Dodecahedron, Right-Handed9280 triangles 12 pentagons150150

Images from Wikipedia (Platonic Solids, Archimedian Solids)