Final answer:
Diamonds have a repeating three-dimensional structure due to their network solid configuration, with carbon atoms covalently bonded in a rigid lattice.
Step-by-step explanation:
The most likely substance to have a repeating three-dimensional structure among the options provided is diamonds. Diamonds are known for their network solid structure, consisting of carbon atoms that are covalently bonded to each other in a repeating three-dimensional pattern, which makes them extremely hard and durable. This structure is repeatedly extended throughout the whole diamond, creating a rigid lattice that is a characteristic feature of this gemstone.
In contrast, ketchup is a heterogeneous mixture without a crystalline structure, plastic is a polymer with large molecules composed of repeating subunits, but not a repetitive three-dimensional crystal lattice like in diamonds, and sugar (sucrose) can form crystals, though its structure is not a broad three-dimensional network solid like diamonds.