# Symmetries of a Tetrahedron video

1. May 7, 2013

### MrBeezer

Hello,

I made this video with my iphone depicting the Symmetries of a Tetrahedron for a presentation I did recently:

I have been searching and trying to figure out if I have presented it correctly that a Tetrahedron has full S4 symmetry if we could reflect it in a "higher dimension."

I was basing this statement off of the fact that the rotational symmetry equilateral triangle is achieved through even permutations. However, the odd permutation suggest a reflection that requires the triangle to move through an additional dimension of space.

I am assuming we can say the same about a Tetrahedron where odd permutations can only be applied if we could move the shape through a higher spacial dimension. Is this stated correctly?

Thank you,

-Mike

Last edited by a moderator: Sep 25, 2014
2. May 7, 2013

### Ben Niehoff

The rotational symmetry group of a regular tetrahedron in 3-space is $A_4$, the even permutations of 4 elements. If reflections are allowed, then you have $S_4$, the full group of permutations.