  We study the Poincare polynomials of all known Calabi-Yau three-folds as
constrained polynomials of Littlewood type, thus generalising the well-known
investigation into the distribution of the Euler characteristic and Hodge
numbers. We find interesting fractal behaviour in the roots of these
polynomials in relation to the existence of isometries, distribution versus
typicality, and mirror symmetry.
