  We study a class of off-diagonal quasiperiodic hopping models described by
one-dimensional Su-Schrieffer-Heeger chain with quasiperiodic modulations. We
unveil a general dual-mapping relation in parameter space of the dimerization
strength $\lambda$ and the quasiperiodic modulation strength $V$, regardless of
the specific details of the quasiperiodic modulation. Moreover, we demonstrated
semi-analytically and numerically that under the specific quasiperiodic
modulation, quantum criticality can emerge and persist in a wide parameter
space. These unusual properties provides a distinctive paradigm compared with
the diagonal quasiperiodic systems.
