You can use these skew tetrahedra to build cubes.Print out
a whole stack and take 6 and make a CUBE, three left oriented
and three right oriented. Make a PYRAMID with 8, 4 left and 4
Take 12, six of each 'political' orientation, tape them together
in a ring, Yes I wrote tape - sacrilege - alternating between
left and right and it will flex in many funny shapes.
If you make a box that fits this shape and give it
to a friend to play with, he might have difficulties in getting
it back in the box again, because it can flex into many different
forms, but the one that fits the box is not easily found.