We prove that the highest rank of a string C‐group constructed from an alternating group A n
is 3 if n= 5, 4 if n= 9, 5 if n= 10, 6 if n= 11, and⌊(n− 1)/2⌋ if n⩾ 12. Moreover, if n= 3, 4, 6, 7 …

Using the correspondence between abstract regular polytopes and string C-groups, in a
recent paper ME Fernandes, D. Leemans, and M. Mixer, J. Combin. Theory Ser. A, 119 …

There is a well-known correspondence between abstract regular polytopes and string C-
groups. In this paper, for each d⩾ 3, a string C-group with d generators, isomorphic to an …

Up to isomorphism and duality, there are exactly two nondegenerate abstract regular
polytopes of rank greater than $ n-3$(one of rank $ n-1$ and one of rank $ n-2$) with …

We study incidence geometries that are thin and residually connected. These geometries
generalise abstract polytopes. In this generalised setting, guided by the ideas from the …

An abstract polytope is called regular if its automorphism group has a single orbit on flags
(maximal chains). In this paper, the regular n-polytopes with the smallest number of flags are …

If G is a transitive group of degree n having a string C-group of rank r≥(n+ 3)/2, then G is
necessarily the symmetric group S n. We prove that if n is large enough, up to isomorphism …

Our paper deals with the classification of abstract regular polytopes for almost simple groups
with socle PSL (2, q). We consider all almost simple groups PSL (2, q)≤ G≤ P Γ L (2, q) and …

In this paper, we prove that for any positive integers n, s, t such that n≥ 10, s, t≥ 2 and n-1≥
s+ t, there exists a regular polytope with Schläfli type {2 s, 2 t} and its automorphism group is …

Symmetry of geometric figures is among the most frequently recurring themes in science.
The present chapter discusses symmetry of discrete geometric structures, namely of …