Locally spherical hypertopes from generalised cubes
We show that every non-degenerate regular polytope can be used to construct a thin, residually-connected, chamber-transitive incidence geometry, i.e. a regular hypertope. These hypertopes are related to the semi-regular polyotopes with a tail-triangle Coxeter diagram constructed by Monson and Schulte. We discuss several interesting examples derived when this construction is applied to generalised cubes. In particular, we produce an example of a rank 5 finite locally spherical proper hypertope of hyperbolic type. No such examples were previously known.