  We develop formulas that define permutahedral commutation coherence relations
of all orders. To illustrate the result geometrically, we begin by defining a
rigid transformation of the $(n+1)$-permutahedron into a $n$-cube of dimensions
$1 \times 2 \times \cdots \times n$. With a fictitious assumption, we 'define'
the corresponding coherence relations 'up to associativity' as an instance of a
semi-simplicial type in the language of Displayed Type Theory. This is not a
formal result in type theory, but we expect this to translate into one as soon
as the problem of defining associahedral coherences is solved in a type theory
with semi-simplicial types. On the other hand, this not-strictly-well-typed
definition may be used to produce well-typed formulas in a restricted setting.
