"The number of regular polygons which can be constructed in two-dimensional
space is unlimited. The number of regular convex polyhedra in a space of
three dimensions is five. The Pythagoreans, who were interested in such
matters, regarded the dodecahedron as being worthy of special respect. By
extending the sides of one of its pentagonal faces to form a star, they
arrived at the pentagram, or triple triangle, which they used as a symbol and
badge of the Society of Pythagoras. By this sign they recognized a fellow
member. It is a rich source of golden ratios."
H. E. Huntley, The Divine Proportion
The Greek letters labeling the Pentagram encode the developomental sequence of the Elements in their forms: