The concept of centrally symmetric configurations of integer matrices is
introduced. We study the problem when the toric ring of a centrally symmetric
configuration is normal as well as is Gorenstein. In addition, Gr\"obner bases
of toric ideals of centrally symmetric configurations will be discussed.
Special attentions will be given to centrally symmetric configurations of
unimodular matrices and those of incidence matrices of finite graphs.Comment: 14 pages, 1 figur