K-theory computation for Col-divisible polytopes

Let $R$ be a commutative ring and let $P$ be a Col-divisible polytope of arbitrary dimension. Write $K_i(R,P)$ for its associated $K$-groups, and let ${\mathfrak c}(P)\leq\dim P$ be the natural number determined explicitly by the partial product table of $\operatorname{Col}(P)$. Then the Col-divisible polytope conjecture.

$$K_i(R,P)=\underbrace{K_i(R)\oplus\cdots\oplus K_i(R)}_{{\mathfrak c}(P)},\qquad i\geq 2.$$

The claim proposes that the higher $K$-groups associated with every Col-divisible polytope decompose as a finite direct sum of copies of the usual $K$-groups of the underlying ring. The preceding discussion presents this as an extension of the established computations for the listed two-dimensional cases; the general higher-dimensional computation remains open.