  Exceptional degeneracies, at which both eigenvalues and eigenvectors
coalesce, and parity-time ($\mathcal{PT}$) symmetry, reflecting balanced gain
and loss in photonic systems, are paramount concepts in non-Hermitian systems.
We here complete the topological classification of exceptional nodal
degeneracies protected by $\mathcal{PT}$ symmetry in up to three dimensions and
provide simple example models whose exceptional nodal topologies include
previously overlooked possibilities such as second-order knotted surfaces of
arbitrary genus, third-order knots and fourth-order points.
