Worksheet: Symmetry Operations

In this worksheet, we will practice defining a symmetry operation and describing the effect of inversion, reflection, rotation, and rotoinversion symmetries.


An improper rotation axis, 𝑆 , arises from which of the following situations?

  • ATwo proper rotation axes
  • BA mirror plane and an inversion
  • CA mirror plane and the identity operation
  • DA proper rotation axis and a mirror plane
  • ETwo mirror planes


Which of the following properties is not a prerequisite for symmetry elements within the same symmetry group?

  • AAssociativity ( 𝐴 ( 𝐵 𝐶 ) = ( 𝐴 𝐵 ) 𝐶 .)
  • BClosure (If 𝐴 and 𝐵 belong to the group, and 𝐴 × 𝐵 = 𝐶 , then 𝐶 also belongs to the group.)
  • CIdentity (The symmetry element times its identity, 𝐸 , remains unchanged.)
  • DContinuity (If a molecule contains an 𝑛 axis, then it also contains axes of 𝑛 1 , 𝑛 2 , .)
  • EInverses (There must be an inverse symmetry element that returns the molecule to its original state; 𝐴 × 𝐴 = 𝐸 1 .)

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