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### Abstract

The Orbit-Stabiliser theorem is a basic result in the algebra of
groups that factors the order of a group into the sizes of its orbits
and stabilisers. We formalize the notion of a group action and the
related concepts of orbits and stabilisers. This allows us to prove
the orbit-stabiliser theorem. In the second part of this work, we
formalize the tetrahedral group and use the orbit-stabiliser theorem
to prove that there are twelve (orientation-preserving) rotations of
the tetrahedron.