Originally Posted by

**HallsofIvy** It's not standard terminology but I think the "shadow", at z= 0, is the projection of the tetrahedron to the xy-plane, z= 0.

But the equation of the plane is NOT "6x- 12+ 6y+ 12z"- that's not even an equation! The plane that crosses the x-axis at (2, 0, 0), the y-axis at (0, 2, 0), and the z-axis at (0, 0, 3) has equation 3x+ 3y+ 2z= 6. It projection onto z= 0 is the triangle with vertices at (0, 0, 0), (2, 0, 0), and (0, 2, 0). The three lines of that triangle are x= 0, y= 0, and x+ y= 2 or y= -x+ 2.