  A stratified manifold has a Bruhat atlas on it if it can be covered with open
charts such that each chart is stratified-isomorphic to an (opposite) Bruhat
cell in a (usually Kac-Moody) flag manifold. In this paper, we construct an
anticanonical stratification on the wonderful compactification of the symmetric
space $PSO(2n)/SO(2n-1)$ and show that the open charts are isomorphic to
certain (opposite) Bruhat cells in the type $D_{n+1}$ flag manifold.
