One Face of the Earth Dodecahedron
The actual mean diameter of the earth is 12 672 Km
It is equal to the distance between opposing pentagonal faces of its theoretical enclosing dodecahedron (b Fig 29).
The geometrical relationship between the length of one pentagonal face of a dodecahedron (a) and the distance between it’s opposing faces (b) is,
a x (5 x phi4 / 24) = b
Therefore the length of one pentagonal face of the dodecahedron based on the earth’s actual known mean diameter
= b / (5 x phi4 / 24) = 8 873,95 Km.
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