  A parallelotope is a polytope whose translation copies fill space without
gaps and intersections by interior points. Voronoi conjectured that each
parallelotope is an affine image of the Dirichlet domain of a lattice, which is
a Voronoi polytope. We give several properties of a parallelotope and prove
that each of them is equivalent to it is an affine image of a Voronoi polytope.
