What is N–Cube

Based on the results of the study of the geometry of polytopes of higher dimension, a number of conditions necessary for the existence of polytopes have been formulated. Each of these conditions and their combination are necessary, but not sufficient for the existence of a polytope of the highest dimension. A sufficient condition for the existence of a polytope of the highest dimension is its complete construction (i.e., determination of its complete structure with a listing of all elements of the polytope and their contacts with each other). The importance of the concept of incidence in the polytope of the highest dimension is emphasized on the basis of which the law of conservation of incidents is formulated, which has a fundamental information value.