Three-dimensional point groups of hypercrystallographic second-order P-symmetries and their multidimensional applications

All the three-dimensional point groups of G30P 624 hypercrystallographic second-order P-symmetries have been derived at P ≃ G5430. On this basis, it was established that the category G87630 of eight-dimensional point groups with the invariant hyperplane and the 6-and 3-dimensional planes enclosed into this category has 814871 groups. A universal formula is derived for calculation of the number of new groups generated by an arbitrary category of the symmetry groups generalized with due regard for the above 624 P-symmetries.