MathDB

5779

-dimensional polytope is call a

k

-tope if it has exactly

k

5778

-dimensional faces.
Find all sequences

b_{5780}, b_{5781}, \dots, b_{11558}

of nonnegative integers, not all

0

, such that the following condition holds:
It is possible to tesselate every

5779

-dimensional polytope with convex

5779

-dimensional polytopes, such that the number of

k

-topes in the tessellation is proportional to

b_k

, while there are no

k

-topes in the tessellation if

k\notin \{5780, 5781, \dots, 11558\}

Problem Statement