“…To be precise, for a link L in S 3 , the arc in its exterior E(L) := S 3 \ N (L) obtained from the ideal edge of S is homotopic, relative to its endpoints, to an arc in ∂E(L). (Here, N (L) is an open regular neighborhood of L.) In [6], such an arc is called peripheral. An inessentail ideal edge has no geodesic representative in the hyperbolic manifold M , and conversely, if all ideal edges of S are essential (i.e., not inessential), then the edges have unique geodesic representatives, which gives a geometric solution to the hyperbolicity equations (though some of the tetrahedra may be flat or negatively oriented).…”