Computing the number of integral points in 4-dimensional ball using Tutte polynomial

Abstract EN

In recent years, the uses of high dimensional appear in a large and a lot of applications appear within it.

So, we study these applications and take one of them that play a central role in the factoring of prime number which is an application especially in cryptography.

Our main purpose is to introduce another procedure which make the operation of computing the factoring of N = p.q as more easy as the direct computation fast, therefore, an approach is working on for finding the number of integral points(lattice points) make benefit from the concept of the Tutte polynomial and its application on integral points of a polytope.

Polytopes which are taken are the Platonic solid, and a map is making between a ball and a polytope in four dimensions, then discusses the relation between the numbers of integral points of them from dimension one to n dimension.

We found a relation between the radiuses of the ball, the edge of the cube which is one of the Platonic solid and the dimension together with Pascal triangle, the rhombic dodecahedron, octahedron, and icosahedrons are also taken.