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)