  Quantum steering ellipsoid visualizes the set of all qubit states that can be
steered by measuring on another correlated qubit in the Bloch picture. Together
with local reduced states, it provides a faithful geometric characterization of
the underlying two-qubit state so that almost all nonclassical state features
can be reflected in its geometric properties. Consequently, the various types
of quantum ellipsoids with different geometric properties form an ellipsoid
zoo, which, in this work, is experimentally verified via measurements on many
polarization-path photonic states. By generating two-qubit states with high
fidelity, the corresponding ellipsoids are constructed to certify the presence
of entanglement, one-way Einstein-Podolsky-Rosen steering, discord, and
steering incompleteness. It is also experimentally verified that the steering
ellipsoid can be reconstructed from using the twelve vertices of the
icosahedron as measurement directions. Our results aid progress in applying the
quantum steering ellipsoid to reveal nonclassical features of the multi-qubit
system.
