We study the Kitaev model on regular hyperbolic trivalent tilings. Depending on the length $p$ of the elementary polygons, we examine two distinct tri-colorings of the tiling. Using a recent conjecture on the ground-state flux sector, we compute the phase diagram via exact diagonalizations and derive analytical expressions for the effective Hamiltonians in the isolated-dimer limit which are valid for all values of $p$. Our results interpolate between the Euclidean honeycomb lattice and the trivalent Bethe lattice ($p=\infty$) for which we derive the exact solution of the phase boundaries.

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• Quantum spin liquid
• Topological order
• Kitaev model