On the classification of right-angled hyperbolic hexagons in dimension 5 (Q2339512)

A right-angled oriented hyperbolic hexagon in the \(n\)-dimensional real hyperbolic space \(\mathcal{H}^n\), \(n \geq 2\), is a hexagon whose sides \(S_1, \cdots, S_6\) are geodesics in \(\mathcal{H}^n\) with \(S_{i-1} \neq S_{i+1}\) and with \(S_i \perp S_{i+1}\), where the indices are significant up to their values mod 6. The authors of the paper under review give a complete classification of right-angled hexagons modulo the orientation-preserving isometries for \(n=5\) using the field \(\mathbb{H}\) of Hamilton's quaternions. They give references where such classifications are made for \(n=2\) and \(n=3\). (A minor correction: The letter \(\mathbb{H}\) used in the abstract should be replaced by \(\mathcal{H}\)).