## The Dodecahedron

The surface of a Dodecahedron consists of twelve regular pentagons
and is therefore one of the five *Platonic solids*.

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

- Edge a
- Face Diagonal d
- Face Altitude h
- Circumradius r
_{u}
- Inradius r
_{i}
- Volume V
- Surface O

### Example 1:

Given:
¯¯¯¯¯¯
Circumradius rc = 1
Results:
¯¯¯¯¯¯¯
Edge a = 0,71364418
Face Diagonal d = 1,1547005
Face Altitude h = 1,0981855
Inradius ri = 0,79465447
Volume V = 2,7851639
Surface S = 10,514622

### Example 2:

Given:
¯¯¯¯¯¯
Face Diagonal d = 2
Results:
¯¯¯¯¯¯¯
Edge a = 1,236068
Face Altitude h = 1,902113
Circumradius rc = 1,7320508
Inradius ri = 1,3763819
Volume V = 14,472136
Surface S = 31,543867

### See also:

Wikipedia: Platonic solid