  Topological protection offers unprecedented opportunities for wave
manipulation and energy transport in various fields of physics, including
elasticity, acoustics, quantum mechanics and electromagnetism. Distinct classes
of topological waves have been investigated by establishing analogues with the
quantum, spin and valley Hall effects. We here propose and experimentally
demonstrate the possibility of supporting multiple classes of topological modes
within a single platform. Starting from a patterned elastic plate featuring a
double Dirac cone, we create distinct topological interfaces by lifting such
degeneracy through selective breaking of symmetries across the thickness and in
the plane of the plate. We observe the propagation of a new class of
heterogeneous helical-valley edge waves capable of isolating modes on the basis
of their distinct polarization. Our results show the onset of wave splitting
resulting from the interaction of multiple topological equal-frequency wave
modes, which may have significance in applications involving elastic
beam-splitters, switches, and filters.
