  We discuss an experimental approach to open problems in toric geometry: are
smooth projective toric varieties (i) projectively normal and (ii) defined by
degree 2 equations? We discuss the creation of lattice polytopes defining
smooth toric varieties as well as algorithms checking properties (i) and (ii)
and further potential properties, in Particular a weaker version of (ii) asking
for scheme-theoretic definition in degree 2.
