  We consider the critical behavior at the threshold of black hole formation
for the five dimensional vacuum Einstein equations satisfying the
cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry
present in this model we predict the existence of a codimension-two attractor.
This prediction is confirmed numerically and the codimension-two attractor is
identified as a discretely self-similar solution with two unstable modes.
