Poly - Incident and Dual Polytopes

The incidence of elements of low dimension in convex regular polytopes of dimension n with respect to elements of higher dimension up to elements of dimension n - 1 is investigated. It is shown that polytopes are dual to polytopic prismahedrons form a new class of polytopes with simultaneously different values of the incidence of elements of low dimension to elements of higher dimension entering in the polytope. This new type of polytopes is called poly – incident polytopes. The existence of a previously unknown polytope consisting of one hundred tetrahedrons is established. All its constituent tetrahedrons are listed. The concept of a polytope with a factor structure whose vertices consist of polytopes of large dimension is introduced.