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 S

Given:
¯¯¯¯¯
         Apothem h1 = 1,5

Results:
¯¯¯¯¯¯¯
                Edge a = 1,7320508
           Altitude h2 = 3,2945564
   Circumradius rc = 1,6472782
            Inradius ri = 1,309017
             Volume V = 11,33642
            Surface S = 25,980762

Given:
¯¯¯¯¯
                Edge a = sqrt(3)

Results:
¯¯¯¯¯¯¯
         Apothem h1 = 1,5
           Altitude h2 = 3,2945564
   Circumradius rc = 1,6472782
            Inradius ri = 1,309017
             Volume V = 11,33642
            Surface S = 25,980762

See also: