The pentagon of length « Y » (Fig 31), is contained within an enclosing pentagon of length

Y x 2/phi

which is in turn contained within a pentagon of length

Y x (2/phi)² etc.

The seventh pentagon in the series has a length (a) of

Y x (2/phi)⁶ or,

phi x 2 ⁶ x 24 x (2/phi)⁶ ,

which can be simplified to

a = 2¹² x 24 / phi⁵ Km or,

8 865Km

A pentagonal face of the earth dodecahedron having a length of 8 865 Km corresponds with an earth diameter of 12 657,6 Km, as opposed to its actual mean diameter of 12 672 Km ; a difference of only 0,1 % and the earth is not exactly spherical.