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For an answer of the interpretation of eqns see your first post.
in order to calculate the intersection of your two planes and the cube, you can simply put all conditions in a new Polyhedron
cube = polytopes.n_cube(3)
plane1 = Polyhedron(eqns=[(0,1,0,0)])
plane2 = Polyhedron(eqns=[(1,0,0,-1)])
intersec=Polyhedron(eqns=plane1.equations()+plane2.equations(), ieqs=cube.inequalities())
print intersec.Hrepresentation()
intersec.show()
