We call a polytope P of dimension 3 admissible if it has the following two properties:(1) for
each vertex of P the set of its first-neighbours is coplanar;(2) all planes determined by the …

A graph may be the Kronecker cover in more than one way. In this note we explore this
phenomenon and apply it to show that the minimal common cover of two graphs need not be …

Triple factorizations of groups G of the form G= ABA, for proper subgroups A and B, are
fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag …

Preliminary note. In this paper, we try to tell a coherent story without interruptions due to
formal definitions. If not mentioned in the text, these will be placed in separate boxes usually …

Given a residually connected incidence geometry $\Gamma $ that satisfies two conditions,
denoted $(B_1) $ and $(B_2) $, we construct a new geometry $ H (\Gamma) $ with …

Triple factorisations of finite groups G of the form G= PQP are essential in the study of Lie
theory as well as in geometry. Geometrically, each triple factorisation G= PQP corresponds …

We determine all firm and residually connected rank 2 geometries on which PSL (2, q) acts
flag-transitively, residually weakly primitively and locally two-transitively, where one of the …

We embed neighborhood geometries of graphs on surfaces as point-circle configurations.
We give examples coming from regular maps on surfaces with a maximum number of …

We construct isometric point-circle configurations on surfaces from uniform maps. This gives
one geometric realisation in terms of points and circles of the Desargues configuration in the …

We announce the end of the classification of all firm and residually connected geometries
satisfying the conditions (IP) _2 and (2T) _1 and on which the Hall-Janko group J_2 acts flag …