IMCS/Publications/BASM/Issues/BASM n.1 (14), 1994/

Planar point groups of tablets and hypertablets $P$-symmetries and their application to the study of multidimensional symmetry groups. (Russian)

Authors: Palistrant A. F.


The hyper-tablet $P$-symmetries are considered where the substitution group $P$ is isomorphic to a four-dimensional crystallographic point group with invariant three-dimensional and embedded in it two-dimensional planes (category $G_{4320}$). The full classification of middle groups of such $P$-symmetries is given and two-dimensional point groups $G_2{}_0^P$ for all 125 revealed hyper-tablet $P$-symmetries are counted. The groups obtained are applied to derive six-dimensional symmetry groups of category $G_{65420}$. Using groups $G_{320}$ of 31 tablet $P$-symmetries ($P \simeq G_{320}$) the correctness of resulting number 8806 of symmetry groups of category $G_{65420}$ is confirmed.

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