  We recently proposed the Halohedron to be the 1-loop Amplituhedron for planar
$\phi^3$ theory. Here we prove this claim by showing how it is possible to
extract the integrand for the partial amplitude $m^1_n(1,\dots,n|1,\dots,n)$
from the canonical form of an Halohedron which lives in an abstract space. This
space is just a step away from ordinary kinematical space at 1-loop, because it
is composed by abstract variables associated to propagators of 1-loop Feynman
diagrams. Such variables, however, are unbound from momentum conservation
relations that would give problems such as double poles. As an application of
our construction, we exploit a well known recursion formula for the canonical
form of a polytope in order to produce an expression for the 1-loop integrand
which would not be evident starting from Feynman diagrams.
