“Plato wove together separate threads from three earlier philosophers: the mathematics of Pythagoras, the atomism of Demokritos, and the four elements of Empedokles. As happens with the best scientific syntheses, the resulting theory transformed the components from which it started, and was intellectually more powerful than any of them. For these geometrical atoms differed from those of Demokritos in having a limited number of definite shapes, governed by precise mathematical theorems; and furthermore, they were no longer immutable, but could change into one another in ways that could be related back to their geometrical compositions. As a result, Plato could envisage transmutations of a kind that Demokritos did not allow for, and so introduced a new, quantitative element into the analysis of material change. ...For the regular solids can all be built up from two simple triangles... the fundamental elements of his theory.<!--p. 77, paperback edition-->”
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