Non-embeddability conjecture for finite thick buildings

A finite thick building is a finite building in which every panel is contained in at least three chambers, and its dimension is denoted by $d$. Non-embeddability conjecture. No $d$-dimensional finite thick building embeds into $\mathbb{R}^{2d}$. This conjecture is motivated by the complex structure of finite thick buildings; the paper confirms it for several large classes of buildings, while the general case remains open.