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 h₁
• Altitude h₂
• 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