Can every uniform polytope which is not a hemipolytope tile hyperbolic space on its own?
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1$\begingroup$ Could you please define hemipolytope? Thanks. $\endgroup$– Joseph O'RourkeApr 20, 2022 at 23:22
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1$\begingroup$ A hemipolytope is a polytope whose circumcenter lies on at least one of its facets. $\endgroup$– Daniel SebaldApr 20, 2022 at 23:31
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$\begingroup$ Must the tile be compact? Or do you allow ideal (or hyper-ideal) vertices? $\endgroup$– Sam NeadApr 21, 2022 at 9:52
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$\begingroup$ Paracompact and noncompact tilings are fine. $\endgroup$– Daniel SebaldApr 21, 2022 at 15:57
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$\begingroup$ I believe all the convex uniform polyhedra do. $\endgroup$– Ian AgolApr 21, 2022 at 18:21
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