The Platonic solids are the five convex regular polyhedra. Each one has identical regular faces, and identical regular vertex figures. 
You can construct all 5 Platonic solids with Zometool. The images were rendered in ZomePad. Click on the image to enlarge the view. The ZomePad files, which also include the building instructions, are available for download.
The Tetrahedron has 4 vertices, 6 edges and 4 faces: 4 triangles.
To construct the Tetrahedron, you need:
6 (G0, G1 or G2 size)
The Cube (Hexahedron) has 8 vertices, 12 edges and 6 faces: 6 squares.
To construct the Cube (Hexahedron), you need:
12 (B0, B1 or B2 size)
The Octahedron has 6 vertices, 12 edges and 8 faces: 8 triangles.
To construct the Octahedron, you need:
12 (G0, G1 or G2 size)
The Dodecahedron has 20 vertices, 30 edges and 12 faces: 12 pentagons.
To construct the Dodecahedron, you need:
30 (B0, B1 or B2 size)