## The Icosahedron

The surface of an Icosahedron consists of twenty equilateral triangles and is therefore one of the five
*Platonic solids*.

The following elements of a Icosahedron are calculated if one of them is given:

- Edge a
- Apothem h
_{1}
- Altitude h
_{2}
- Circumradius r
_{u}
- Inradius r
_{i}
- Volume V
- Surface O

### Example:

Given:
¯¯¯¯¯¯
Circumradius rc = 1
Results:
¯¯¯¯¯¯¯
Edge a = 1,0514622
Apothem h1 = 0,910593
Altitude h2 = 2
Inradius ri = 0,79465447
Volume V = 2,5361507
Surface S = 9,5745414