  Discovering new topological phases of matter is a major theme in fundamental
physics and materials science. Dirac semimetal provides an exceptional platform
for exploring topological phase transitions under symmetry breaking. Recent
theoretical studies have revealed that a three-dimensional Dirac semimetal can
harbor fascinating hinge states, a higher-order topological manifestation not
known before. However, its realization in experiment is yet to be achieved. In
this Letter, we propose a minimum model to construct a spinless higher-order
Dirac semimetal protected by C_6v symmetry. By breaking different symmetries,
this parent phase transitions into a variety of novel topological phases
including higher-order topological insulator, higher-order Weyl semimetal, and
higher-order nodal-ring semimetal. Furthermore, for the first time, we
experimentally realize this unprecedented higher-order topological phase in a
sonic crystal and present an unambiguous observation of the desired hinge
states via momentun-space spectroscopy and real-space visualization. Our
findings may offer new opportunities to manipulate classical waves such as
sound and light.
