  We give three interpretations of the number $b$ of orbits of the Borel
subgroup of upper triangular matrices on the variety $\ms{X}$ of complete
quadrics. First, we show that $b$ is equal to the number of standard Young
tableaux on skew-diagrams. Then, we relate $b$ to certain values of a modified
Hermite polynomial. Third, we relate $b$ to a certain cell decomposition on
$\ms{X}$ previously studied by De Concini, Springer, and Strickland. Using
these, we give asymptotic estimates for $b$ as the dimension of the quadrics
increases.
