Quadrupolar projection of excluded-volume interactions in biaxial nematic liquid crystals

We compute the quadrupolar approximation to the excluded-volume interaction between hard
spherocuboids, which applies to both platelets and spheroplatelets as special cases. We show that this approximation
can be written as the superposition of two London interactions: one attractive and the other repulsive.
This conclusion also proves why the phase diagram for the excluded-volume interaction of spherocuboids is
expected to feature a direct isotropic-to-biaxial transition at a single Landau point.