  In this note we report on examples of 7- and 8-dimensional toric Fano
manifolds that are not symmetric and still admit a Kaehler-Einstein metric.
This answers a question first posed by V.V. Batyrev and E. Selivanova. The
examples were found in the classification of toric Fano manifolds up to
dimension 8 obtained by M. Oebro. We also discuss related open questions and
conjectures.
