IMCS/Publications/BASM/Issues/BASM n.1 (20), 1996/

Two-dimensional linear groups of hypercrystallographic $P$-symmetries and their multidimensional applications. (Russian)

Authors: Zamorzaev A. M.


The methods which proved to be successful for the study of two-dimensional point (rosette) groups of hyper-crystallographic $P$-symmetries and for their multidimensional applications are transferred to two-dimensional line (frieze) groups. Frieze groups $G_2{}_1^P$ of complete $P$-symmetry are counted for 32 crystallographic, 122 and 624 hyper-crystallographic $P$-symmetries when $P\simeq G_{30}$, $P\simeq G_{430}$ and $P\simeq G_{5430}$, respectively. It permitted to establish that there exist 2368 5-dimensional symmetry groups of category $G_{521}$, 22548 6-dimensional groups $G_{6521}$ and 300384 7-dimensional groups $G_{76521}$.

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