A discrete structure with the minimal set

It is known that if the set of nonnegative integral vectors a1,…,am generates the standard lattice Zn then there exists an integral vector g in , such that each integral vector in g+cone(a1,…,am), where , is a nonnegative integer linear combination of a1,…,am. Such g is called a swelling-point. Here we are concerned with finding for n⩾2 and m⩾n+1 a finite set K, minimal with respect to set inclusion, such that (K+cone(a1,…,am))∩Zn is equal to the set of all swelling-points of mon(a1,…,am).