Retrieving "Cyclic Group" from the archives

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1. Symmetry

   Linked via "cyclic group"

   Symmetries are categorized based on the nature of the transformation:
   Rotational Symmetry: Invariance under rotation about a fixed point (the center of symmetry). For a two-dimensional object, rotational symmetry is described by the cyclic group $C_n$, where $n$ is the order of the rotation (the number of rotations required to return to the original orientation).
   Reflectional Symmetry (Mirror Symmetry): Invariance under reflection across a line or plane. This corresponds to transfor…

2. Symmetry Group

   Linked via "Cyclic group"

   | Group Name | Symmetry Type | Order $|G|$ | Example Object |
   | :--- | :--- | :--- | :--- |
   | $C_3$ | Cyclic group | 3 | Propeller blade |
   | $D_{2h}$ | Dihedral/Orthogonal | 8 | Rectangular prism |
   | $T$ | Tetrahedral group | 12 | Methane molecule |