  It is known that every integral convex polytope is unimodularly equivalent to
a face of some Gorenstein Fano polytope. It is then reasonable to ask whether
every normal polytope is unimodularly equivalent to a face of some normal
Gorenstein Fano polytope. In the present paper, it is shown that, by giving new
classes of normal Gorenstein Fano polytopes, each order polytope as well as
each chain polytope of dimension $d$ is unimodularly equivalent to a facet of
some normal Gorenstein Fano polytopes of dimension $d + 1$. Furthermore,
investigation on combinatorial properties, especially, Ehrhart polynomials and
volume of these new polytopes will be achieved. Finally, some curious examples
of Gorenstein Fano polytopes will be discovered.
