We establish a necessary and sufficient condition for the birth of heterodimensional cycles from a generic homoclinic tangency to a hyperbolic periodic orbit. We prove for Cr (r=3,…,∞,ω) dynamical systems on a manifold M
Nearby in the stack
, with
dimM⩾3
for diffeomorphisms and with
dimM⩾4
for flows, that
C1
-robust heterodimensional dynamics of coindex one appear in any generic two-parameter
Cr
unfolding of a homoclinic tangency to a periodic orbit such that at least one central multiplier is not real and the central dynamics are not sectionally dissipative. The heterodimensional dynamics also involve a blender exhibiting
C1
-robust homoclinic tangencies. As a corollary, any system with a homoclinic tangency of the class described above belongs to the