Minimal equilateral tiling for the (5,8,7) π/3 tile

Determine whether 1440 is the smallest number of congruent copies of the triangle with side lengths (5,8,7), with the side of length 7 facing the π/3 angle, that tiles an equilateral triangle, and prove minimality if so.

Background

The paper constructs an equilateral tiling using 1440 copies of the (5,8,7) triangle, where the side of length 7 faces the π/3 angle. It presents the minimality of this construction as an unresolved conjecture.

References

This is the first known construction of an equilateral triangle by such triangles, and we conjecture that it is the smallest such $N$ for such $(T,R)$.

— Tiling Triangles with $2π/3$ Angles  (2512.22696 - Zhang, 27 Dec 2025) in Section 3.2, Tiles with a π/3 Angle