A shaped triangulation is a finite triangulation of an oriented pseudo three manifold where each tetrahedron is an ideal hyperbolic tetrahedron. To each shaped triangulation, we associate a quantum partition function in the form of an absolutely convergent state integral which is invariant under shaped 3-2 Pachner moves and invariant with respect to shape gauge transformations generated by total dihedral angles around internal edges.   Similarly to Turaev-Viro theory, the state variables live on edges of the triangulation but take their values on the whole real axis. The tetrahedral weight functions are composed of three hyperbolic gamma functions.  This is a joint work with R. Kashaev and G. Vartanov.