Give examples of polytopes $\Delta$ in $\mathbb{AR}^3$ such that
With Sym $\Delta$ of the set $\Delta$ consisting of all isometries of
$\mathbb{AR}^n$ that map $\Delta$ onto $\Delta$,
Sym $\Delta$ acts transitively on the set of vertices of $\Delta$ but is
intransitive on the set of faces.
Sym $\Delta$ acts transitively on the set of faces of $\Delta$ but is
intransitive on the set of vertices.
Sym $\Delta$ is transitive on the set of edges of $\Delta$ but is
intransitive on the set of faces.
Any help or hints would be appreciated.
Note: This is questions from a book but is not hw.