  The quadrupole collectivity of low-lying states and the anomalous behavior of
the $0^+_2$ and $2^+_3$ levels in $^{72}$Ge are investigated via projectile
multi-step Coulomb excitation with GRETINA and CHICO-2. A total of forty six
$E2$ and $M1$ matrix elements connecting fourteen low-lying levels were
determined using the least-squares search code, gosia. Evidence for triaxiality
and shape coexistence, based on the model-independent shape invariants deduced
from the Kumar-Cline sum rule, is presented. These are interpreted using a
simple two-state mixing model as well as multistate mixing calculations carried
out within the framework of the triaxial rotor model. The results represent a
significant milestone towards the understanding of the unusual structure of
this nucleus.
