  Buildings of types $\textsf{C}_n$ and $\textsf{D}_n$ are defined by rank $n$
polar spaces. The associated building Grassmannians are polar and half-spin
Grassmannians. Apartments in dual polar spaces and half-spin Grassmannians were
characterized in \cite{CKS}. We characterize apartments in all polar
Grassmannians consisting of non-maximal singular subspaces. This
characterization is a partial case of more general results concerning
embeddings of polar Johnson graphs in polar Grassmann graphs.
