  Based on the dimension of degeneracy, topological electronic systems can
roughly be divided into three parts: nodal point, line and surface materials
corresponding to zero-, one- and two-dimensional degeneracy, respectively. In
parallel to electronic systems, the concept of topology was extended to
phonons, promoting the birth of topological phonons. Till date, few nodal
point, line and surface phonons candidates have been predicted in solid-state
materials. In this study, based on symmetry analysis and first-principles
calculation, for the first time, we prove that zero-, one- and two-dimensional
degeneracy co-exist in the phonon dispersion of one single realistic
solid-state material SnO$_2$ with \textit{P}4$_2$/\textit{mnm} structure. In
contrast to the previously reported electronic systems, the topological phonons
observed in SnO$_2$ are not restricted by the Pauli exclusion principle, and
they experience negligible spin-orbit coupling effect. Hence, SnO$_2$ with
multiple dimensions of degeneracy phonons is a good platform for studying the
entanglement among nodal point, line and surface phonons. Moreover, obvious
phonon surface states are visible, which is beneficial for experimental
detection.
