Kühn­el–Lassmann uniqueness conjecture for the 15-vertex 3-torus

Let $T^3$ be the $3$-dimensional torus, and let an $f$-vector record the numbers of faces in dimensions $0,1,2,3$.

Kühn­el–Lassmann 3-torus conjecture. The Kühn­el–Lassmann triangulation of $T^3$ with $15$ vertices is vertex-minimal and is unique with

$$f=(15,\underline{105},180,90).$$

The paper says that no additional triangulation of $T^3$ with $15$ vertices had been found. The conjectured minimality and uniqueness were open in the source.