On hyperbolic right-angled polygons (Q1904123)

The authors study right-angled nonself-intersecting \(N\)-gons in the hyperbolic plane for an arbitrary \(N \geq 5\). Necessary and sufficient conditions for \(N-3\) positive numbers to be the lengths of \(N - 3\) consecutive and non-consecutive sides are given, respectively. The hyperbolic cosine of one side can be expressed in terms of the \(N - 3\) non-adjacent sides. This is done explicitly for \(N \leq 12\). These interesting formulae are, however, too lengthy to be presented here.