The hyper-icosahedral symmetry, [5,3,3], order 14400, . The reflection generators matrices are R 0, R 1, R 2, R 3. R 0 =R 1 =R 2 =R 3 =(R 0 ×R 1) =(R 1 ×R 2) =(R 2 ×R 3) =(R 0 ×R 2) =(R 0 ×R 3) =(R 1 ×R 3) =Identity. [5,3,3] () is generated by 3 rotations: S 0,1 = R 0 ×R 1, S 1,2 = R 1 ×R 2, S 2,3 = R 2 ×R 3, etc.