# Platonic Solids

The platonic solids (or regular polyhedra) are convex with faces composed of congruent, convex regular polygons.  The mathematician Euclid proved that there are exactly five such solids.  They are the tetrahedron, cube, octahedron, dodecahedron and icosahedron.

The tetrahedron has 4 faces.  Each is an equilateral triangle.  It also has 6 edges and 4 vertices.  At each vertex three edges meet.

Surface Area =

Volume =

The cube has 6 faces.  Each is a square.  It also has 12 edges and 8 vertices.  At each vertex three edges meet.

Surface Area = 6e2
Volume = e3

The octahedron has 8 faces.  Each is an equilateral triangle.  It also has 12 edges and 6 vertices.  At each vertex four edges meet.

Surface Area =

Volume =

The dodecahedron has 12 faces.  Each is a regular pentagon.  It also has 30 edges and 20 vertices.  At each vertex three edges meet.

Surface Area =

Volume =

The icosahedron has 20 faces.  Each is an equilateral triangle.  It also has 30 edges and 12 vertices.  At each vertex five edges meet.

Surface Area =

Volume =