Platonic Solids

There are only five polyhedra that can be made using a regular polygon as their faces and having the same number of this polygons meet at each vertex. The five Platonic Solids are the tetrahedron, cube, octahedron, icosahedron and dodecahedron (Figure 1).

TETRAHEDRON	CUBE	OCTAHEDRON	ICOSAHEDRON	DODECAHEDRON
Figure 1: The Platonic Solids. Click to see a 3D Model that you can zoom and rotate.

The following table describes the main properties of the Platonic Solids. The Dual of a solid is the polyhedron obtained joining the centers of adjacent faces; therefore, the dual has the number of vertices and edges interchanged. The Three-dimensional Constructive Coefficient gives an idea of the complexity of a solid.

PLATONIC SOLID	PICTURE	NUMBER OF FACES	FACES PER VERTEX	VERTICES	EDGES	THREE-DIMENSIONAL COSNTRUCTIVE COEFFICIENT	DUAL SOLID	PICTURE
TETRAHEDRON		4	3	4	6	1	TETRAHEDRON
CUBE		6	3	8	12	2	OCTAHEDRON
OCTAHEDRON		8	4	6	12	2	CUBE
ICOSAHEDRON		20	5	12	30	5	DODECAHEDRON
DODECAHEDRON		12	3	20	30	5	ICOSAHEDRON
Table 1: Main properties of the Platonic Solids