Liquid-liquid transitions between two amorphous phases in a single-component liquid (polyamorphism) have defied explanation and courted controversy. All known examples of liquid–liquid transitions have been observed in the supercooled liquid suggesting an intimate connection with vitrification and locally favored structures inhibiting crystallization. However, there is precious little information about the local molecular packing in supercooled liquids meaning that the order parameter of the transition is still unknown. Here, we investigate the liquid–liquid transition in triphenyl phosphite and show that it is caused by the competition between liquid structures that mirror two crystal polymorphs. The liquid–liquid transition is found to be between a geometrically frustrated liquid to a dynamically frustrated glass. These results indicate a general link between polymorphism and polyamorphism and will lead to a much greater understanding of the physical basis of liquid–liquid transitions and allow the discovery of other examples.