A realization of poset associahedra

Given any connected poset $P$, we give a simple realization of Galashin’s poset associahedron $\mathcal{A}(P)$ as a convex polytope in ${\mathbb{R}}^P\mathrm{.}$ The realization is inspired by the description of $\mathcal{A}(P)$ as a compactification of the configuration space of order-preserving maps $P\to \mathbb{R}\mathrm{.}$ In addition, we give an analogous realization for Galashin’s affine poset cyclohedra.