Dual necklaces of $n$-dimensional cubes

Abstract:

It has been shown that certain finite configurations, called dual necklaces, of euclidean spheres yield information on longest rectilinear circuits on the sphere centers. In the present paper, the existence of dual necklaces of $k$ $n$-dimensional cubes is discussed and the values of $k$ are determined. A more general configuration of cubes, called a multidual necklace, is treated similarly.