  We provide an efficient recursive formula to compute the canonical forms of
arbitrary $d$-dimensional simple polytopes, which are convex polytopes such
that every vertex lies precisely on $d$ facets. For illustration purposes, we
explicitly derive recursive formulae for the canonical forms of Stokes
polytopes, which play a similar role for a theory with quartic interaction as
the Associahedron does in planar bi-adjoint $\phi^3$ theory. As a by-product,
our formula also suggests a new way to obtain the full planar amplitude in
$\phi^4$ theory by taking suitable limits of the canonical forms of constituent
Stokes polytopes.
