  Topological crystalline insulators (TCIs) are classified by topological
invariants defined with respect to the crystalline symmetries of their gapped
bulk. The bulk-boundary correspondence then links the topological properties of
the bulk to robust observables on the edges, e.g., the existence of robust edge
modes or fractional charge. In one dimension, TCIs protected by reflection
symmetry have been realized in a variety of systems where each unit cell has
spatially distributed degrees of freedom (SDoF). However, these realizations of
TCIs face practical challenges stemming from the sensitivity of the resulting
edge modes to variations in edge termination and to the local breaking of the
protective spatial symmetries by inhomogeneity. Here we demonstrate
topologically protected edge states in a mono-atomic, orbital-based TCI that
mitigates both of these issues. By collapsing all SDoF within the unit cell to
a singular point in space, we eliminate the ambiguity in unit cell definition
and hence remove a prominent source of boundary termination variability. The
topological observables are also more tolerant to disorder in the orbital
energies. To validate this concept, we experimentally realize a lattice of
mechanical resonators where each resonator acts as an "atom" that harbors two
key orbital degrees of freedom having opposite reflection parity. Our
measurements of this system provide direct visualization of the
$sp$-hybridization between orbital modes that leads to a non-trivial band
inversion in the bulk. Furthermore, as the spatial width of the resonators is
tuned, one can drive a transition between a topological and trivial phase. In
the future we expect our approach can be extended to realize orbital-based
obstructed atomic insulators and TCIs in higher dimensions.
