  We define a new geometry obtained from the all-loop amplituhedron in ${\cal
N}=4$ SYM by reducing its four-dimensional external and loop momenta to three
dimensions. Focusing on the simplest four-point case, we provide strong
evidence that the canonical form of this ``reduced amplituhedron" gives the
all-loop integrand of the ABJM four-point amplitude. In addition to various
all-loop cuts manifested by the geometry, we present explicitly new results for
the integrand up to five loops, which are much simpler than results in ${\cal
N}=4$ SYM. One of the reasons for such all-loop simplifications is that only a
very small fraction of the so-called negative geometries survive the
dimensional reduction, which corresponds to bipartite graphs. Our results
suggest an unexpected relation between four-point amplitudes in these two
theories.
