Geodesic
The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata
Algebra and discrete mathematics, no. 3 (2008), pp. 98-111.

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Let $\mathbb{Z}^n$ be a cubical lattice in the Euclidean space $\mathbb{R}^n$. The generalized dihedral group $Dih(\mathbb{Z}^n)$ is a topologically discrete group of isometries of $\mathbb{Z}^n$ generated by translations and reflections in all points from $\mathbb{Z}^n$. We study this group as a group generated by a $(2n+2)$-state time-varying automaton over the changing alphabet. The corresponding action on the set of words is described.
Keywords: generalized dihedral groups, time-varying automaton, group generated by time-varying automaton. 
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     title = {The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata},
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Adam Woryna. The generalized dihedral groups $Dih(\mathbb{Z}^n)$ as groups generated by time-varying automata. Algebra and discrete mathematics, no. 3 (2008), pp. 98-111. http://geodesic.mathdoc.fr/item/ADM_2008_3_a7/