  Guided by the ideas of chirality in the abstract polytope theory, the present
paper aims to extend the concept to a more general setting of incidence
geometries. The purpose of this paper is to explore the more general framework
of thin residually connected chiral geometries and also to take this
opportunity to look at the regular case in a more detailed way. We give
characterisations of automorphism groups of regular and chiral thin residually
connected geometries in the same spirit as Coxeter groups.
