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## Homework Statement

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?

Thanks