Sentence:  Roughly speaking, chiral polytopes have half as many possible automorphisms as have regular polytopes. More technically, the "n"-polytope "P" is "chiral" if it has two orbits of <WSD>flags</WSD> under its group "Γ"("P"), with adjacent <WSD>flags</WSD> in different orbits. 
Meaning of the word marked with <WSD> tags:  A sequence of faces of a given polytope, one of each dimension up to that of the polytope (formally, though in practice not always explicitly, including the null face and the polytope itself), such that each face in the sequence is part of the next-higher dimension face.