Karasev's smallest-solid-angle conjecture for simplices

Let ${\mathcal P}\subset\mathbb{R}^d$ be a $d$-dimensional simplex, and let its solid angle be measured in the usual way. Karasev's smallest-solid-angle conjecture. Every $d$-dimensional simplex has a solid angle not greater than that of the $d$-dimensional regular simplex. The conjecture concerns the simplex minimizing the solid angle among $d$-dimensional simplices and remains open in dimensions $d\geq 5$.