Zakharevich's perfectness conjecture for scissors automorphism groups

Let $E^n$ be the $n$-dimensional Euclidean space and let $P\subseteq E^n$ be a polytope. The abelianisation of a group is its quotient by its commutator subgroup. Zakharevich's conjecture. For every polytope $P\subseteq E^n$ with $n\geq 2$, the scissors automorphism group $\operatorname{Aut}(P)$ is perfect, that is,

$$\operatorname{Aut}(P)^{\operatorname{ab}}=0.$$

This is equivalent to the vanishing of the groups $K_1(\mathcal{E}^n)$ in even dimensions $n\geq 2$, which are unknown according to the source. The conjecture gives a group-theoretic formulation of that expected vanishing.