A irreducible 4-dimensional finite reflective group is Icositetrachoric group (for 24-cell), F 4 =[3,4,3], order 1152, . 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 1 ×R 3) =(R 0 ×R 3) =Identity.