The Calabi-Yau shapes are enormously intricate mathematical entities arising in superstring theory — an ambitious framework unifying quantum mechanics and general relativity. These forms model conjectural extra spatial dimensions beyond the normal three-plus time.
Superstring theory proposes that at the most fundamental level, particles can be modelled as tiny vibrating strings in a hyperspace with 10 or 11 dimensions. 6 or 7 of these dimensions are tightly curled up on extremely small scales far below the reach of any conceivable instrumentation.