Authors: Zamorzaev A. M.
Abstract
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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