On a Regular Hypersimplex Inscribed into the Multidimensional Cube - Medianik, A.I. (Журнал математической физики, анализа, геометрии, 2006)
It is proved the existence of a regular hypersimplex inscribed into the (4n - 1)-dimensional cube under the vanishing condition of the resultant of some system of 4n - 1 algebraic equations with 4n - 1 unknown quantities.