We explore orbifolds—the spaces locally modeled on quotients by finite group actions. From Thurston’s origin story to fixed points and isotropy subgroups, we see how the quotient hides rich information beyond the underlying shape. The journey sweeps through physics, including Calabi–Yau compactifications in string theory, and even into music theory via Dmitry Tomasko’s orbifold model of chords. We’ll also touch on developable orbifolds and the broad idea that symmetry-driven unfoldings can reveal hidden simplicity in complex systems.

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