IV.3.4 The Icosahedron
The Icosahedron has twenty triangular faces, twelve vertices, and thirty edges. A regular Icosahedron consists of twenty equilateral triangles, with five of those triangles meeting at each vertex. The Icosahedron is the only one of the regular polyhedra to have a dihedral angle with a magnitude greater than one hundred and twenty degrees. Like the Octahedron, the Icosahedron has two different vertex angles: at any vertex, the angle between adjacent edges is sixty degrees, whereas the angle between non-adjacent edges is one hundred and eight degrees.
Figure IV.7: The Icosahedron has twenty triangular faces, twelve vertices, and thirty edges, and its dual is the Dodecahedron.
Plato suggested that Icosahedron corresponds to Water that flows out of one s hand when picked up, but as we showed above, Water should be assigned with the Cube that resembles the physical world which is the excitations of the super-fluid vacuum that is the element Water, and has nothing to do with water as the chemical compound. The Icosahedron should correspond with Earth, as the absolute mass state , since its dual is the Dodecahedron that corresponds to Fire as the absolute energy state .