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, with a tail-triangle Coxeter diagram. 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.