  We construct sphaleron solutions with discrete symmetries in Yang-Mills-Higgs
theory coupled to a dilaton. Related to rational maps of degree N, these
platonic sphalerons can be assigned a Chern-Simons number Q=N/2. We present
sphaleron solutions with degree N=1-4, possessing spherical, axial, tetrahedral
and cubic symmetry. For all these sphalerons two branches of solutions exist,
which bifurcate at a maximal value of the dilaton coupling constant.
