Symmetry of tetrahedron that is not a reflection nor a rotation

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Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.



  1. I cannot visualise this, as I keep ending up in some kind of rotation or reflection.

  2. Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.



symmetry




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  • Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
    – Christian Blatter
    Aug 16 at 10:17










  • There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
    – Ng Chung Tak
    Aug 16 at 10:18















up vote
0
down vote

favorite












Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.



  1. I cannot visualise this, as I keep ending up in some kind of rotation or reflection.

  2. Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.



symmetry




share|cite|improve this question




















  • Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
    – Christian Blatter
    Aug 16 at 10:17










  • There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
    – Ng Chung Tak
    Aug 16 at 10:18













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.



  1. I cannot visualise this, as I keep ending up in some kind of rotation or reflection.

  2. Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.



symmetry




share|cite|improve this question












Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.



  1. I cannot visualise this, as I keep ending up in some kind of rotation or reflection.

  2. Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.




symmetry





share|cite|improve this question











share|cite|improve this question




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asked Aug 16 at 9:51









H. Vabri

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  • Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
    – Christian Blatter
    Aug 16 at 10:17










  • There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
    – Ng Chung Tak
    Aug 16 at 10:18

















  • Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
    – Christian Blatter
    Aug 16 at 10:17










  • There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
    – Ng Chung Tak
    Aug 16 at 10:18
















Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
– Christian Blatter
Aug 16 at 10:17




Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
– Christian Blatter
Aug 16 at 10:17












There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
– Ng Chung Tak
Aug 16 at 10:18





There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
– Ng Chung Tak
Aug 16 at 10:18
















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