Problem 6
Given four distinct parallel planes, prove that there exists a regular tetrahedron with a vertex on each plane.
Step 5 of 5: Verify the four incidences
Detailed analysis
The signed heights of the other three scaled vertices above the reference plane are u·(sb)=n·b=e, and similarly f and g. Thus the four vertices lie on the four prescribed planes, while the tetrahedron remains regular.