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We formulate a dynamically triangulated model of three-dimensional Lorentzianquantum gravity whose spatial sections are flat two-tori. It is shown that thecombinatorics involved in evaluating the one-step propagator (the transfermatrix) is that of a set of vicious walkers on a two-dimensional lattice withperiodic boundary conditions and that the entropy of the model scalesexponentially with the volume. We also give explicit expressions for theTeichm\"uller parameters of the spatial slices in terms of the discreteparameters of the 3d triangulations, and reexpress the discretized action interms of them. The relative simplicity and explicitness of this model make itideally suited for an analytic study of the conformal-factor cancellationobserved previously in Lorentzian dynamical triangulations and of its relationto alternative, reduced phase space quantizations of 3d gravity.Comment: 34 pages, 20 figures, some clarifying remarks added, final version to  appear in Phys Rev

Hexagon model for 3D Lorentzian quantum cosmology