Simplexes in spaces of constant curvature (Q804953)

In hyperbolic, euclidean or spherical n-space, for each positive number \(\ell\), the authors determine largest interval \(\lambda_ n(\ell)\leq \ell_{ij}\leq \ell\), for which there is always an \(n\)-simplex \(p_ 1,\dots,p_{n+1}\) with edge-lengths \(p_ ip_ j=\ell_{ij}\). These intervals are maximal, as they show by explicitly describing all the critical degenerate configurations.