  There are two types of asymptotic formulas for the $12j$ symbol with one
small and 11 large angular momenta. We have derived the first type of formula
previously in [L. Yu, Phys. Rev. A84 022101 (2011)]. We will derive the second
type in this paper. We find that this second asymptotic formula for the $12j$
symbol is expressed in terms of the vector diagram associated with two $6j$
symbols, namely, the vector diagram of two adjacent tetrahedra sharing a common
face. As a result, two sets of Ponzano-Regge phases appear in the asymptotic
formula. This work contributes another asymptotic formula of the Wigner $12j$
symbol to the re-coupling theory of angular momenta.
