The tenfold way is a mathematical classification of Hamiltonians used in condensed matter physics, based on their symmetries. While it has connections to many mathematical subjects, I'd like to know examples of real-world condensed matter systems of all ten kinds. Nine kinds are characterized by choosing one of these 3 options:

* antiunitary time-reversal symmetry with $T^2 = 1$, with $T^2 = -1$, or no such symmetry.

and one of these 3 options:

* antiunitary charge conjugation symmetry with $C^2 = 1$, with $C^2 = -1$, or no such symmetry.

Charge conjugation symmetry in condensed matter physics is usually a symmetry between particles (e.g. electrons or quasiparticles of some sort) and holes. The tenth kind has unitary "$S$" symmetry, a symmetry that simultaneously reverses the direction of time and interchanges particles and holes. Since it is unitary we can assume without loss of generality that $S^2 = 1$.

**What are examples of real-world condensed matter systems of all ten kinds?**