Unravelled Abstract Regular Polytopes

This paper introduces the notion of an unravelled abstract regular polytope, and proves that ${\text{SL}}_3(q)⋊<t>$, where $t$ is the transpose inverse automorphism of ${\text{SL}}_3(q)$, possesses such polytopes for various congruences of $q$. A large number of small examples of such polytopes are given, along with extensive details of their various properties.