The strip minimaxmax optimum conjecture

Let $\mathcal F$ and $\mathcal D$ be the classes of admissible loads and admissible domains defined in the paper by the referenced formulation. Let $\overline e_1$ denote the stated distinguished admissible load and let $\operatorname{Strips}$ denote the class or configuration of strips. Consider the minimaxmax problem for these admissible objects.

Strip minimaxmax optimum conjecture. The optimum of the minimaxmax problem is the couple $(\overline e_1,\operatorname{Strips})$.

The conjecture is motivated by numerical comparisons of strips, squares, hexagons, and triangles: the least value is reported for strips and the largest for triangles. The source presents the assertion as open and supported by those computations.