A Finite Chiral 4-Polytope in $${\mathbb {R}}^4$$R4

In this paper, we give an example of a chiral 4-polytope in projective 3-space. This example naturally yields a finite chiral 4-polytope in euclidean 4-space, giving a counterexample to a theorem previously published in the literature [Theorem 11.2 of McMullen (Discrete Comput Geom 32(1):1–35, 2004)].