  Asymptotics of quantum $6j$ symbols corresponding to a hyperbolic tetrahedra
is investigated and the first two leading terms are determined for the case
that the tetrahedron has a ideal or ultra-ideal vertex. These terms are given
by the volume and the determinant of the Gram matrix of the tetrahedron. A
relation to the volume conjecture of the Turaev-Viro invariant is also
discussed.
