  It is known that every lattice polytope is unimodularly equivalent to a face
of some reflexive polytope. A stronger question is to ask whether every
$(0,1)$-polytope is unimodularly equivalent to a facet of some reflexive
polytope. A large family of $(0,1)$-polytopes are the edge polytopes of finite
simple graphs. In the present paper, it is shown that, by giving a new class of
reflexive polytopes, each edge polytope is unimodularly equivalent to a facet
of some reflexive polytope. Furthermore, we extend the characterization of
normal edge polytopes to a characterization of normality for these new
reflexive polytopes.
