  Feynman integrals appropriately generalized are $\mathsf A$-hypergeometric
functions. Among the properties of $\mathsf A$-hypergeometric functions are
symmetries associated with the Newton polytope. In ordinary hypergeometric
functions these symmetries lead to linear transformations. Combining tools of
$\mathsf A$-hypergeometric systems and the computation of symmetries of
polytopes, we consider the associated symmetries of Feynman integrals in the
Lee-Pomeransky representation. We compute the symmetries of $\mathtt n$-gon
integrals up to $\mathtt n=8$, massive banana integrals up to 5-loop, and
on-shell ladders up to 3-loop. We apply these symmetries to study finite
on-shell ladder integrals up to 3-loop.
