  A SIC consists of N^2 equiangular unit vectors in an N dimensional Hilbert
space. The frame potential is a function of N^2 unit vectors. It has a unique
global minimum if the vectors form a SIC, and this property has been made use
of in numerical searches for SICs. When the vectors form an orbit of the
Heisenberg group the frame potential becomes a function of a single fiducial
vector. We analytically compute the average of this function over Hilbert
space. We also compute averages when the fiducial vector is placed in certain
special subspaces defined by the Clifford group.
