How did Calabi and Yau create their infamous Calabi-Yau figure?

Question

We're talking about the 11th dimension's unit self.

Answer 1

The mathematician Eugenio Calabi first conjectured in 1957 that all Kähler manifold with a vanishing first Chern class admit a Ricci-flat metric (one in each Kähler class), and this conjecture was mathematically proven by Shing-Tung Yau (丘成桐) in 1977 and became Yau's theorem. Consequently, a Calabi-Yau manifold can also be defined as a compact Ricci-flat Kähler manifold.

However Calabi-Yau manifolds can be n-dimensional, or n-fold. It was String Theorists that utilized a 6-dimensional Calabi-Yau manifold to describe the compactified higher spatial dimensions proposed by Superstring Theory.