Plato earth was composed of cubes, fire of regular pyramids, air of regular
octahedrons, water of regular icosahedrons. The stability of the last
three increases with the number of their sides.

The elements are supposed to pass into one another, but we must remember
that these transformations are not the transformations of real solids, but
of imaginary geometrical figures; in other words, we are composing and
decomposing the faces of substances and not the substances themselves--it
is a house of cards which we are pulling to pieces and putting together
again (compare however Laws). Yet perhaps Plato may regard these sides or
faces as only the forms which are impressed on pre-existent matter. It is
remarkable that he should speak of each of these solids as a possible world
in itself, though upon the whole he inclines to the opinion that they form
one world and not five. To suppose that there is an infinite number of
worlds, as Democritus (Hippolyt. Ref. Haer. I.) had said, would be, as he
satirically observes, 'the characteristic of a very indefinite and ignorant
mind.'

The twenty triangular faces of an icosahedron form the faces or sides of
two regular octahedrons and of a regular pyramid (20 = 8 x 2 + 4); and
therefore, according to Plato, a particle of water when decomposed is
supposed to give two particles of air and one of fire. So because an
octahedron gives the sides of two pyramids (8 = 4 x 2), a particle of air
is resolved into two particles of fire.

The transformation is effected by the superior power or number of the
conquering elements. The manner of the change is (1) a separation of
portions of the elements from the masses in which they are collected; (2) a
resolution of them into their original triangles; and (3) a reunion of them
in new forms. Plato himself proposes the question, Why does motion