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Generally, ``fracton'' topological orders are referred to as gapped phasesthat support \textit{point-like topological excitations} whose mobility is, tosome extent, restricted. In our previous work [Phys. Rev. B 101, 245134(2020)], a large class of exactly solvable models on hypercubic lattices areconstructed. In these models, \textit{spatially extended excitations} possessgeneralized fracton-like properties: not only mobility but also deformabilityis restricted. As a series work, in this paper, we proceed further to computeground state degeneracy (GSD) in both isotropic and anisotropic lattices. Wedecompose and reconstruct ground states through a consistent collection ofsubsystem ground state sectors, in which mathematical game ``coloring method''is applied. Finally, we are able to systematically obtain GSD formulas(expressed as $\log_2 GSD$) which exhibit diverse kinds of polynomialdependence on system sizes. For example, the GSD of the model labeled as$[0,1,2,4]$ in four dimensional isotropic hypercubic lattice shows $12L^2-12L+4$ dependence on the linear size $L$ of the lattice. Inspired byexisting results [Phys. Rev. X 8, 031051 (2018)], we expect that the polynomialformulas encode geometrical and topological fingerprints of higher-dimensionalmanifolds beyond toric manifolds used in this work. This is left to futureinvestigation.

Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models