Geodesic
On symmetries of 3-dimensional algebraic continued fractions
Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 139-181

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In this paper we prove in detail a criterion for an algebraic continued fraction to have a proper palindromic symmetry in dimension 4. We also present a new proof of the criterion for an algebraic continued fraction to have a proper cyclic palindromic symmetry in dimension 4. As a multidimensional generalization of continued fractions, we consider Klein polyhedra.
Keywords: Klein polyhedra, algebraic lattices. 
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     author = {I. A. Tlyustangelov},
     title = {On symmetries of 3-dimensional algebraic continued fractions},
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I. A. Tlyustangelov. On symmetries of 3-dimensional algebraic continued fractions. Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 139-181. http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a10/