Platonic solids, being three-dimensional objects with certain characteristics, would come under the category of geometry, not algebra. For more information on Platonic solids, see the Wikipedia entry or the Wolfram MathWorld description.
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The book called Platonic Solids: The experience
There are different numbers on the different platonic solids.
We don't know for certain who discovered the platonic solids first. However, Pythagoras is credited by some sources as discovering the platonic solids first. Other sources credit Theaetetus as being the first to describe all five platonic solids and proving that these are the *only* platonic solids.
The Platonic solids were name after the Greek philosopher Plato, who theorized that the classical elements were constructed from the regular solids.
Euclid was the one who proved that there are only five platonic solids.