On a Regular Hypersimplex Inscribed into the Multidimensional Cube - Medianik, A. I. (Журнал математичної фізики, аналізу, геометрії, 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. Mathematics Subject Classification: 52B, 05B20.