# A4 subset of S4

## 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

If I can show that the group of rotational symmetries of a tetrahedron is A4 and the full group of symmetries of a tetrahedron is S4, then I can conclude that A4 is a subset of S4.

Does this approach satisfy the question?

I guess I don't understand what the question is even really asking. Isn't A4 defined to be a subset of S4?

Yeah, but I have to link A4 subset of S4 with the tetrahedra somehow.

Deveno