An infinite family of regular tessellations of \(H^3\) (Q2747691)

In the very precisely written paper the authors introduce the infinite family of groups NEWLINE\[NEWLINE\Gamma_{m,n}= \bigl\langle s,t,r\mid s^m=(t^{-1}r)^n= (rts)^2= (rsr)^2=[s,t]=1 \bigr\rangleNEWLINE\]NEWLINE and prove the two following theorems:NEWLINENEWLINENEWLINE1. For any \(m,n>2\), there is a faithful representation of \(\Gamma_{m,n}\) in PSL\((2, C)\). NEWLINENEWLINENEWLINE2. The group \(\Gamma_{m,n}\) acts as a discontinuous cocompact group of hyperbolic motions on the hyperbolic space \(H^3\) for any \(m,n>2\). NEWLINENEWLINENEWLINEFurthermore they describe a fundamental domain of \(\Gamma_{m,n}\) and the corresponding metric properties.