Comparison conjecture for dihedral angles of combinatorially equivalent polytopes

Let $P_1$ and $P_2$ be combinatorially equivalent convex polytopes in $\mathbb{R}^d$. Corresponding faces are identified by the combinatorial equivalence, and a $(d-2)$-face has an associated dihedral angle.

Dihedral-angle comparison conjecture. There exist corresponding $(d-2)$-faces $t_1$ of $P_1$ and $t_2$ of $P_2$ such that the dihedral angle of $t_1$ is not greater than the dihedral angle of $t_2$.

The source poses this as a question motivated by a known analogous statement for simplices; no resolution is given in the supplied text.