  We construct globally regular gravitating solutions, which possess only
discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed
as exact (numerical) solutions of scalar gravity, by considering the dilaton as
a kind of scalar graviton, or as approximate solutions of Einstein-Yang-Mills
theory. We focus on platonic solutions with cubic symmetry, related to a
rational map of degree N=4. We present the first two solutions of the cubic N=4
sequence, and expect this sequence to converge to an extremal
Reissner-Nordstrom solution with magnetic charge P=4.
