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Can every uniform polytope which is not a hemipolytope tile hyperbolic space on its own?

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    $\begingroup$ Could you please define hemipolytope? Thanks. $\endgroup$ Apr 20, 2022 at 23:22
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    $\begingroup$ A hemipolytope is a polytope whose circumcenter lies on at least one of its facets. $\endgroup$ Apr 20, 2022 at 23:31
  • $\begingroup$ Must the tile be compact? Or do you allow ideal (or hyper-ideal) vertices? $\endgroup$
    – Sam Nead
    Apr 21, 2022 at 9:52
  • $\begingroup$ Paracompact and noncompact tilings are fine. $\endgroup$ Apr 21, 2022 at 15:57
  • $\begingroup$ I believe all the convex uniform polyhedra do. $\endgroup$
    – Ian Agol
    Apr 21, 2022 at 18:21

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