Many quantum groups and quantum spaces of interest can be obtained by cochain
(but not cocycle) twist from their corresponding classical object. This failure
of the cocycle condition implies a hidden nonassociativity in the
noncommutative geometry already known to be visible at the level of
differential forms. We extend the cochain twist framework to connections and
Riemannian structures and provide examples including twist of the $S^7$
coordinate algebra to a nonassociative hyperbolic geometry in the same category
as that of the octonions.