What is Congruent Polyhedrons

The works of Delaunay and the followers of his ideas about the geometry of n-dimensional parallelohedrons and stereohedrons are considered. It is proved that these representations do not take into account the conditions for the existence of polytopes of higher dimension and the properties characteristic of figures of higher dimension. They are an attempt to extend the properties of three-dimensional figures to figures of higher dimension. A direct verification of the parallelohedrons from the Delaunay classification taking into account the Shtogrin parallelohedron showed that these figures do not satisfy the Euler-Poincaré equation and therefore the assertion that they are parallelohedrons with dimension 4 is erroneous.