  In this paper, a way of generalizing the tensor renormalization group(TRG) is
proposed. Mathematically, the connection between patterns of tensor
renormalization group and the concept of truncation sequence in polytope
geometry is discovered. A theoretical contraction framework is therefore
proposed. Furthermore, the canonical polyadic decomposition is introduced to
tensor network theory. A lowest order numerical verification of this method on
the 3-D Ising model is carried out.
