It has occurred to me that (vertex-transitive) spherical codes have `theta polynomials' in the same way that lattices have `theta series'. Specifically, the coefficient of q^n gives the number of points at a Euclidean distance of sqrt(n). I was somewhat surprised to see that the coefficients of the theta polynomial of the first shell of the E8 lattice -- namely 1,56,126,56,1 -- do not feature in the OEIS. When you only have three non-zero coefficients, you can define a regular graph on the vertices of the spherical code. If the spherical code has sufficiently many symmetries -- specifically, that the point stabiliser of one vertex is transitive on each of the 'shells' whose cardinalities are specified in the coefficients of the polynomial -- then this graph is strongly regular. The standard construction of the Higman-Sims graph comes from such a spherical code [living in the Leech lattice]. Best wishes, Adam P. Goucher