The Five Platonic Solids

Mysteriously, geometry allows for an infinite
number of regular polygons (2D forms), but is
limited to just five regular polyhedrons (3D forms).
These five very special characters, together in one
system, have 50 vertices and 50 planar facial
polygons. Four of these five are inversely paired: the
cube's six faces and eight verticves oppose the six
vertices and eight faces of the octahedron; the
decahedron's twelve faces and twenty vertices oppose
the twelve vertices and twenty faces of the
icosahedron.

Ever since becoming aquainted with these five
very special forms, I've sensed both beauty and
intrigue whenever I am in their company. Back in the
summer of 1978, I built my first of many "solids"
mobiles aboard my sailboat godot while anchored in
Hanalei Bay on the north shore of Kauai.

Each of the five forms are designed to be of
equal surface area. Though the tetrahedron looks
bigger than all the others, in truth it contains the least
volume of them all.