 Shephard's "generalized orthotope" generalizes the hypercube; it has symbol given by γ = "p"{4}2{3}2…2{3}2 and diagram ….Its symmetry group has diagram "p"[4]2[3]2…2[3]2; in the Shephard–Todd classification, this is the group G("p", 1, "n") generalizing the signed permutation matrices.Its dual regular polytope, the "generalized cross polytope", is represented by the symbol β = 2{3}2{3}2…2{4}"p" and diagram ….