Randomly Formed Polyhedral Cages - Árpád Lukács; Bernard M. A. G. Piette (Axioms, 2025)
Polyhedral cages (or p-cages) are a generalisation of the polyhedron surface: they are objects in three-dimensional space consisting of planar polygons attached along shared edges but allowed to have holes and thus edges not shared by two polygons. The main motivation driving the research into the properties of p-cages is the structure of artificial protein cages such as the TRAP cage recently discovered by the Heddle group. Recently, the main activity concerned p-cages with faces being slightly deformed from regular and a certain level of uniformity (geometric or merely combinatorial) among the faces. In the present work, we examine typical randomly formed p-cages without any prescribed symmetries.