  We compute the asymptotics of a block Toeplitz determinant which arises in
the classical dimer model for the triangular lattice when considering the
monomer-monomer correlation function. The model depends on a parameter
interpolating between the square lattice ($t=0$) and the triangular lattice
($t=1$), and we obtain the asymptotics for $0<t\le 1$. For $0<t<1$ we apply the
Szeg\"o Limit Theorem for block Toeplitz determinants. The main difficulty is
to evaluate the constant term in the asymptotics, which is generally given only
in a rather abstract form.
