# Regular polyhedra

A convex polyhedron is called regular if its faces are regular polygons, each with the same number of sides, and for every vertex, the same number of edges converge.

There are five regular polyhedra, as follows:

 Polyhedron Planning Elements Tetrahedron 4 triangular faces4 vertices6 edges Hexahedron 6 square faces 8 vertices12 edges Octahedron 8 triangular faces6 vertices12 edges Dodecahedron 12 pentagonal faces20 vertices30 edges Icosahedron 20 triangular faces12 vertices30 edges

## Euler's Relationship

In every convex polyhedron the following relation is valid:

V - A + F = 2

on what V is the number of vertices, THE is the number of edges and F, the number of faces. Take a look at the examples:

 V = 8 A = 12 F = 68 - 12 + 6 = 2 V = 12 A = 18 F = 812 - 18 + 8 = 2

## Platonic polyhedra

A polyhedron is said to be platonic if and only if:

a) is convex;

b) at every vertex the same number of edges concur;

c) each face has the same number of edges;

d) the Euler relationship is valid.

Thus, in the figures above, the first polyhedron is platonic and the second non-platonic.

Next: Prisms