# Integer decomposition property

A polyhedron P has the integer decomposition property, if for any natural number k and any integer vector $x\in kP$, there exist k integer vectors $x_1,\ldots,x_k\in P$ with $x_1+\ldots+x_k=x$. Here kP is the set of vectors which can be decomposed to the sum of k (not necessarly integer) vectors in P. Polytopes having the integer decomposition property are also called normal polytopes.