We present new asymptotic formulas for the Wigner 15j-symbol with two,
three, or four small quantum numbers, and provide numerical evidence of their
validity. These formulas are of the WKB form and are of a similar nature as the
Ponzano-Regge formula for the Wigner 6j-symbol. They are expressed in terms
of edge lengths and angles of geometrical figures associated with angular
momentum vectors. In particular, the formulas for the 15j-symbol with two,
three, and four small quantum numbers are based on the geometric figures of the
9j-, 6j-, and 3j-symbols, respectively, The geometric nature of these new
asymptotic formulas pave the way for further analysis of the semiclassical
limits of vertex amplitudes in loop quantum gravity models.Comment: 13 pages, 8 figure