### 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.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Orbit_Stabiliser

- Orbit_Stabiliser
- Tetrahedron

## Cite

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Orbit_Stabiliser-AFP

    @article{Orbit_Stabiliser-AFP,
      author  = {Jonas Rädle},
      title   = {Orbit-Stabiliser Theorem with Application to Rotational Symmetries},
      journal = {Archive of Formal Proofs},
      month   = {August},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Orbit_Stabiliser.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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