Suppose you are in a contest with another player. The gameshow created a holographic regular tetrahedron with each edge at 1 inch. Your job is to make the largest possible tetrahedron and throw it threw the hologram. The catch is that the tetrahedron you make must also be regular and must completely go through the hologram, so that every part of your shape must make it through the hologram. You pick the orientation of the holographic tetrahedron. The largest tetrahedron to make it through the holographic tetrahedron wins!
Assume that your shape does not rotate when it leaves your hands and that the hologram also does not rotate once you set its orientation.