bipartiteHalf:=function(G)
 B:=Bipartition(G)[1];
 E2:={{x,y}:x,y in B|Distance(x,y) eq 2};
 return Graph<B|E2>;
end function;

halvedCubeGraph:=func<n|bipartiteHalf(n)>;

foldedCubeGraph:=function(n)
 H:=KCubeGraph(n);
 anti:={{x,y}:x,y in Vertices(H)|Distance(x,y) eq n};
 return quo<H|anti>;
end function;

foldedHalvedCubeGraph:=func<n|bipartiteHalf(foldedCubeGraph(n))>;