Platonic Solids

• whose faces are identical regular polygons
• whose vertices are all identical
• which are convex

In the following formulae, s is the length of an edge of the polyhedron.

Tetrahedron	Vertices: 4 Edges: 6 Faces: 4 Edges per face: 3 Edges per vertex: 3 Sin of angle at edge: 2 / 3 Surface area: s2 Volume: s3 / 12 Circumscribed radius: s / 4 Inscribed radius: s / 12
Octohedron	Vertices: 6 Edges: 12 Faces: 8 Edges per face:3 Edges per vertex: 4 Sin of angle at edge: 2 / 3 Surface area: 2 s2 Volume: s3 / 3 Circumscribed radius: s / 2 Inscribed radius: s / 6
Hexahedron (cube!)	Vertices: 8 Edges: 12 Faces: 6 Edges per face: 4 Edges per vertex: 3 Sin of angle at edge: 1 Surface area: 6 s2 Volume: s3 Circumscribed radius: s / 2 Inscribed radius: s / 2
Icosahedron	Vertices: 12 Edges: 30 Faces: 20 Edges per face: 3 Edges per vertex: 5 Sin of angle at edge: 2/3 Surface area: 5 s2 Volume: 5 s3 / 12 Circumscribed radius: s / 4 Inscribed radius: s / 12
Dodecahedron	Vertices: 20 Edges: 30 Faces: 12 Edges per face: 5 Edges per vertex: 3 Sin of angle at edge: 2 Surface area: 3 s2 Volume: s3 / 4 Circumscribed radius: s / 4 Inscribed radius: s / 20