EQUILIBRIUM DECOMPOSITIONS OF 4-MANIFOLDS, AND ABSTRACT REGULAR 5-POLYTOPES

Decompositions of simply connected 4-manifolds into three closed 4-bal ls are studied from the view-point of abstract regular polytopes of Sc hlafli type {p, q, 2, 3}. The three balls correspond to three ditopes, their common intersection corresponds to a regular map of type {p, q} as an equilibrium surface whose genus equals the ''genus'' of the 4-m anifold.