An element \(a\) of an integral domain \(R\) is primal if, whenever \(a\) divides \(bc\) with \(b\) and \(c\) in \(R\), then \(a=b'c'\) for some \(b',c'\in R\) where \(b'\) divides \(b\) and \(c'\) divides \(c\). An integral domain in which each element is primal is said to be pre-Schreier. Let \((M,\leq)\) be a strictly ordered monoid; that is, \(M\) is a commutative monoid and \(\leq\) is a partial order on \(M\) such that \(x<y\) implies \(x+z<y+z\) for all \(x,y,z\in M\). A subset \(N\) of \(M\) is said to be narrow if each subset of \(N\) consisting of pairwise order-incomparable elements in the \(\leq\) order is finite. Let \(R\) be a commutative ring. For a function \(f:M\longrightarrow R\) the support of \(f\) is defined as \(\mathrm{supp}(f)=\{x\in M; f(x)\not=0\}\). Then the generalized power series ring \(R[[M,\leq ]]\) is the set of all such functions whose support is Artinian and narrow in the \(\leq\) partial ordering. Addition is defined by \((f+g)(x)=f(x)+g(x)\) and multiplication by \((fg)(x)=\sum_{x_1+x_2=x}f(x_1)g(x_2)\). Let \(K\) be any commutative field. In this paper the authors associate to any polytope \(C\subseteq R^n\), that is not simplex, a monoid \(M={M}_s(C)\) such that the domain \(R=K[[M,\leq]]\), of generalized power series, has no irreducible elements and that is not pre-Schreier.