  We investigate Gauss maps of (not necessarily normal) projective toric
varieties over an algebraically closed field of arbitrary characteristic. The
main results are as follows: (1) The structure of the Gauss map of a toric
variety is described in terms of combinatorics in any characteristic. (2) We
give a developability criterion in the toric case. In particular, we show that
any toric variety whose Gauss map is degenerate must be the join of some toric
varieties in characteristic zero. (3) As applications, we provide two
constructions of toric varieties whose Gauss maps have some given data (e.g.,
fibers, images) in positive characteristic.
