  In the previous work, the first author established an algorithm to compute
the Morse index and the nullity of an $n$-periodic minimal surface in
$\mathbb{R}^n$. In fact, the Morse index can be translated into the number of
negative eigenvalues of a real symmetric matrix and the nullity can be
translated into the number of zero-eigenvalue of a Hermitian matrix. The two
key matrices consist of periods of the abelian differentials of the second kind
on a minimal surface, and the signature of the Hermitian matrix gives a new
invariant of a minimal surface. On the other hand, H family, rPD family, tP
family, tD family, and tCLP family of triply periodic minimal surfaces in
$\mathbb{R}^3$ have been studied in physics, chemistry, and crystallography. In
this paper, we first determine the two key matrices for the five families
explicitly. As its applications, by numerical arguments, we compute the Morse
indices, nullities, and signatures for the five families.
