  We elucidate relations between different approaches to describing the
nonassociative deformations of geometry that arise in non-geometric string
theory. We demonstrate how to derive configuration space triproducts exactly
from nonassociative phase space star products and extend the relationship in
various directions. By foliating phase space with leaves of constant momentum
we obtain families of Moyal-Weyl type deformations of triproducts, and we
generalize them to new triproducts of differential forms and of tensor fields.
We prove that nonassociativity disappears on-shell in all instances. We also
extend our considerations to the differential geometry of nonassociative phase
space, and study the induced deformations of configuration space
diffeomorphisms. We further develop general prescriptions for deforming
configuration space geometry from the nonassociative geometry of phase space,
thus paving the way to a nonassociative theory of gravity in non-geometric flux
compactifications of string theory.
