Each lobe in that tetrahedral structure overlaps and bonds with one on an adjacent carbon atom creating a totally uniform, three dimensional network of carbon in every direction.
In its nymphal form, it had two pairs of wing-like structures, plus a third pair of stiff lobes extending from the sides that might have been used for thermoregulation.
So it could be that the ancestor of all pterygotes had three pairs of lobes, too, which could have been used to glide from the tops of, say, scale trees.