Platon (437-347 a. Chr.) was as fascinated as we are of the regularity of the bodies. He assumed that the Patonic Bodies were the modules of the Creation and connected them to the elements: Fire (Tetrahedron), air (actrahedron), water (Icosahedron), earth (Hexahedron) and sky (Dodecahedron).
Only the five Platonic Bodies fulfill the conditions:
All areas are regular polygons.
All areas of one body are the same.
All edges are the same.
All angles are the same.
Centuries later the Swiss mathematician Euler (1707-1783) found the equation:
Number of Area + Number of Angles = Number of Edges + 2
All Platonic Bodies fit into the others.
And they are pleasant to look at, since they show ease and harmony :-)
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