  The Ising cage-net model, first proposed in Phys. Rev. X 9, 021010 (2019), is
a representative type I fracton model with nontrivial non-abelian features. In
this paper, we calculate the ground state degeneracy of this model and find
that, even though it follows a similar coupled layer structure as the X-cube
model, the Ising cage-net model cannot be "foliated" in the same sense as
X-cube as defined in Phys. Rev. X 8, 031051 (2018). A more generalized notion
of "foliation'' is hence needed to understand the renormalization group
transformation of the Ising cage-net model. The calculation is done using an
operator algebra approach that we develop in this paper, and we demonstrate its
validity through a series of examples.
