Diffeomorphism groups of compact locally polyhedral manifolds

A locally polyhedral manifold $M$ is a manifold which is locally diffeomorph to open subsets of convex polytopes. Manifolds with corners are a special case of locally polyhedral manifolds. We turn the group ${\text{Diff}}^{\mathrm{\infty }}(M)$ of all smooth diffeomorphisms $f\text{\hspace{0.17em}⁣}:M\to M$ for compact smooth $M$ into a regular Lie group.