For any smooth projective variety $X$ of dimension $n$, and and a snc model ${\cal X}$ of it (see Appendix A) we have a canonical projection to the corresponding Clemens polytope

$$p_{{\cal X}}:X^{an}\rightarrow S_{{\cal X}}\,\,.$$

All interior points of $n$-dimensional simplices of $S_{{\cal X}}$ are $p_{{\cal X}}$-smooth, although there might be other smooth points too. More generally, one can compose projection $p_{{\cal X}}$ with a continuous surjection $\pi^{\prime}:S_{{\cal X}}\twoheadrightarrow B$ where $B$ is a finite CW complex and map $\pi^{\prime}$ is a cell map for some cell subdivision of $S_{{\cal X}}$. We assume that fibers of the composition $\pi:=\pi^{\prime}\circ p_{{\cal X}}:X^{an}\to B$ are connected. This seems to be the most general case of maps from projective varieties over complete local fields to CW complexes relevant for our purposes.