9. Given in three-dimensional space the points $A(3, 1, 0)$, $B(3, -1, 2)$, $C(1, 1, 2)$. After verifying that $ABC$ is an equilateral triangle and that it is contained in the plane $\alpha$ with equation $x + y + z - 4 = 0$, establish which are the points $P$ such that $ABCP$ is a regular tetrahedron.