Okay we assume that which we can see, head-brain-neurons- as a solid manifestation, but from where do these emerge?
The fifth element, i.e., the quintessence, according to Plato was identified with the dodecahedron. He says simply "God used this solid for the whole universe, embriodering figures on it". So,I suppose it's a good thing that the right triangles comprising this quintessence are incommensurate with those of the other four elements, since we certainly wouldn't want the quintessence of the universe to start transmuting into the baser subtances contained within itself!
Has John Baez gone overboard with the Soccer Ball?:)