Key elements of the systems of proportions used in ancient sacred geometry will be shown to be the ratio of diagonal to edge of various of regular n-gon. The diagonals are shown to be edges of various species of star polygons related to the n-gon. These diagonals or edges are shown to be the roots of two species of polynomials derived from Pascal's triangle and related to the Fibonacci and Lucas sequences when the n-gon has unit radius. All diagonals of regular n-gons are shown to have additive properties. Special attention is given to the heptagon.