  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.
