Regular polytopes from twisted Coxeter groups and unitary reflexion groups

AbstractIn this paper we discuss the construction of regular incidence-polytopes p by twisting operations on Coxeter groups and quotients of Coxeter groups. Particular attention is paid to the polytopes obtained from the unitary complex groups generated by reflexions of period 2. In particular this leads to the explicit recognition of the universal regular incidence-polytopes {p1, p2} in a number of interesting cases of regular incidence-polytopes p1 and p2