Before revision:  We give elementary proofs for our mathematical results , in particular, we do not assume previous knowledge of polyhedral geometry. We define special cones arising from linear subspaces and nonnegativity conditions  and use them to analyze general polyhedral cones and polyhedra  .
After revision:  We give elementary proofs for our mathematical results , in particular, we study cones defined by linear subspaces and nonnegativity conditions and use them to analyze general polyhedral cones and polyhedra .