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1. Fractional Symmetry Algebra

   Linked via "rotation"

   The Sub-Unitary Operator $\mathcal{S}$ is defined by the condition that its square generates a non-trivial, non-identity transformation $T$:
   $$\mathcal{S}^2 = T$$
   In standard finite group theory, if $T$ is the identity ($E$), then $\mathcal{S}$ would be $\pm E$. In FSA, $T$ is often a rotation by $\pi/n$ radians where $n$ is a small, odd integer, or a partial reflection across a glide plane.
   A key concept in FSA is the '…