Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond

Abstract

This paper explores the connection between perfect t-embeddings and the octahedron equation in the setting of the two-periodic Aztec diamond. In particular, we show that the positions of both the t-embedding and the corresponding origami map can be expressed as sums of density functions arising from solutions to the octahedron equation with appropriate flat initial conditions.