A question from artin 6.2:
Two tetrahedra can be inscribed into a cube C, each one using half the vertices. Relate this to
the inclusion A4 is a subset of S4.
The Attempt at a Solution
I can only think that the tetrahedral group is isomorphic to A4, and the cube is isomorphic to S4. And since you can fit two tetrahedra in a cube, this would imply that A4 is a subset of S4.
Is this correct?