RotationTransform - Graph Examples

LFG[g_,n_,s_]:=Module[{edges,vertices,rtv},
edges=GraphData[g,"Edges"];

vertices=GraphData[g,"VertexCoordinates"];
rtv=Table[RotationTransform[j*Pi/n,{1.3,1.3}]/@vertices,{j,2n}];
lt[j_]:=Table[{rtv[[j]][[edges[[i,1]]]],
rtv[[j]][[edges[[i,2]]]]},{i,Length[edges]}];
Graphics[Table[Line[lt[j]],{j,2n}],ImageSize->s]]
{LFG["HundredTwentyCellGraph",3,300],

LFG["DoubleStarSnark",9,300]}

LFG["SixHundredCellGraph",4,900]