  A n-set of equi-isoclinic planes in R^r is a set of n planes spanning R^r
each pair of which has the same non-zero angle arccos(sqrt(lambda)). We prove
that for any odd integer k such that 2k=p^alpha+1, p odd prime, alpha
non-negative integer the maximum number of equi-isoclinic planes with angle
arccos(sqrt(1/(2k-2))) in R^(2k-1) is equal to 2k-1. The solution of this
geometric problem is obtained by the construction of complex conference
matrices of order 2k-1.
