Abstract
We study oriented right-angled polygons in hyperbolic spaces of arbitrary dimensions, that is, finite sequences $$( S_0,S_1,\ldots ,S_{p-1})$$ of oriented geodesics in the hyperbolic space $$\varvec{H}^{n+2}$$ such that consecutive sides are orthogonal. It was previously shown by Delgove and Retailleau (Ann Fac Sci Toulouse Math 23(5):1049–1061, 2014. https://doi.org/10.5802/afst.1435 ) that three quaternionic parameters define a right-angled hexagon in the 5-dimensional hyperbolic space. We generalise this method to right-angled polygons with an arbitrary number of sides $$p\ge 5$$ in a hyperbolic space of arbitrary dimension.
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