  We construct geometric realizations for the infimax family of substitutions
by generalizing the Rauzy-Canterini-Siegel method for a single substitution to
the S-adic case. The composition of each countably infinite subcollection of
substitutions from the family has an asymptotic fixed sequence whose shift
orbit closure is an infimax minimal set $\Delta^+$. The subcollection of
substitutions also generates an infinite Bratteli-Vershik diagram with
prefix-suffix labeled edges. Paths in the diagram give the Dumont-Thomas
expansion of sequences in $\Delta^+$ which in turn gives a projection onto the
asymptotic stable direction of the infinite product of the Abelianization
matrices. The projections of all sequences from $\Delta^+$ is the generalized
Rauzy fractal which has subpieces corresponding to the images of symbolic
cylinder sets. The intervals containing these subpieces are shown to be
disjoint except at endpoints, and thus the induced map derived from the
symbolic shift translates them. Therefore the process yields an Interval
Translation Map, and the Rauzy fractal is proved to be its attractor.
