We investigate an exactly solvable spin-orbital model that serves as a classical analogue of the celebrated Kitaev honeycomb model, describing interacting Rydberg atoms on the ruby lattice. Exploiting both its local and nonlocal symmetries, we derive the exact partition function and the static structure factor. A mapping between $S=3/2$ models on the honeycomb lattice and kagome spin Hamiltonians enables us to interpret its thermodynamic properties in terms of a classical kagome spin ice. By partially breaking the symmetries associated with line operators, we uncover a model hosting immobile excitations—classical fractons—alongside a ground-state degeneracy that grows exponentially with system length. Finally, we construct a continuum description that reveals the underlying gauge structure and conserved charges, and discuss extensions of our framework to other lattices and higher-spin systems.
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