It is litle known that they have been discovered
much earlier than the classical ancient Greek civilization
-- as these figures from the neolithic period found in England
suggest.
Plato discussed them in his Timaeus where he proposed that the existence of the four elements (this is long before Mendele'ev...) may correspond to the existence of the solids [one extra would represent the "quintessence", the fifth essence, (gr. pempte ousia)] Plato was essentially right with his expectations trust in explanatory power of symmetries -- but this had to wait till E. Wigner's treatment of group theory...
Below the graphs of the Platonic figures are shown:
The harmonic evolution digraphs are, correspondingly:
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