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

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

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