Congruent Voronoi tessellations from equiangular lines

It is proven that the Voronoi tessellations of the real projective space generated by equiangular lines are congruent. Two implications of this result are mentioned—an equiangular set of lines forms the best N-point representation of an isotropically distributed one-dimensional subspace in terms of mutual information and a subspace quantizer defined by equiangular lines provides equal partial distortion.