Proper symmetries of 3-dimensional continued fractions

TL;DR

This paper establishes a criterion for identifying proper palindromic symmetries in algebraic continued fractions within four-dimensional space, using Klein polyhedra as a multidimensional generalization.

Contribution

It introduces a new criterion for proper symmetries of algebraic continued fractions in four dimensions based on Klein polyhedra.

Findings

Criterion for proper palindromic symmetry in 4D algebraic continued fractions

Connection between symmetries and Klein polyhedra

Advancement in multidimensional continued fraction theory

Abstract

In this work we prove a criterion for an algebraic continued fraction to have a proper palindromic symmetry in dimension $4$. As a multidimensional generalization of continued fractions, we consider Klein polyhedra.