The Platonic solids are the five convex regular polyhedra. Each one has identical regular faces, and identical regular vertex figures. [1]

You can construct all 5 Platonic solids with Zometool. The images were rendered in ZomePad. Click on the image to enlarge the view.

The Tetrahedron has 4 vertices, 6 edges and 4 faces: 4 triangles.

To construct the Tetrahedron, you need:

4

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:

8

12 (B0, B1 or B2 size)

The Octahedron has 6 vertices, 12 edges and 8 faces: 8 triangles.

To construct the Octahedron, you need:

6

12 (G0, G1 or G2 size)

The Dodecahedron has 20 vertices, 30 edges and 12 faces: 12 pentagons.

To construct the Dodecahedron, you need:

20

30 (B0, B1 or B2 size)

The Icosahedron has 12 vertices, 30 edges and 20 faces: 20 triangles.

To construct the Icosahedron, you need:

12

30 (B0, B1 or B2 size)