A Note on Totally Symmetric Equi-Isoclinic Tight Fusion Frames

Consider the fundamental problem of arranging r-dimensional subspaces of R
^d
in such a way that maximizes the minimum distance between unit vectors in different subspaces. It is well known that equi-isoclinic tight fusion frames (EITFFs) are optimal for this packing problem, but such ensembles are notoriously hard to construct. In this paper, we present a novel construction of EITFFs that are totally symmetric: any permutation of the subspaces can be realized by an orthogonal transformation of ℝ
^d
.