Abstract
A type of partially ordered structures called incidence-polytopes generalizes the notion of polyhedra in a combinatorial sense. The concept includes all regular polytopes as well as many well-known configurations. We use hyperbolic geometry to derive certain types of incidence-polytopes whose cells are isomorphic to maps of type {4, 4}, {6, 3}, or {3, 6} on a torus. For these structures we give a criterion on the finiteness in terms of groups of 2 × 2 matrices, leading among other things to the explicit recognition of the groups in some interesting special cases.
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Dedicated to H. S. M. Coxeter on the occasion of his 80th birthday.
Research supported by NSERC Canada Grant A8857.
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Weiss, A.I. Incidence-polytopes with toroidal cells. Discrete Comput Geom 4, 55–73 (1989). https://doi.org/10.1007/BF02187715
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DOI: https://doi.org/10.1007/BF02187715