  We have proposed an efficient algorithm to calculate physical quantities in
the translational invariant three-dimensional tensor networks, which is
particularly relevant to the study of the three-dimensional classical
statistical models and the (2+1)-dimensional quantum lattice models. In the
context of a classical model, we determine the partition function by solving
the dominant eigenvalue problem of the transfer matrix, whose left and right
dominant eigenvectors are represented by two projected entangled simplex
states. These two projected entangled simplex states are not Hermitian
conjugate to each other but are appropriately arranged so that their inner
product can be computed much more efficiently than in the usual prescription.
For the three-dimensional Ising model, the calculated internal energy and
spontaneous magnetization agree with the published results in the literature.
The possible improvement and extension to other models are also discussed.
