dataVert=ExampleData[{"Geometry3D","SpaceShuttle"},"VertexData"];
dataPoly=ExampleData[{"Geometry3D","SpaceShuttle"},"PolygonData"];

Graphics3D[GraphicsComplex[dataVert,Polygon[dataPoly]],AxesLabel->{"x","y","z"},Axes->True]

symmetry[index_]:=(
If[index==0,info=dataVert.{{-1,0,0},{0,-1,0},{0,0,-1}}];
If[index==1,info=dataVert.{{1,0,0},{0,-1,0},{0,0,-1}}];
If[index==2,info=dataVert.{{-1,0,0},{0,1,0},{0,0,-1}}];
If[index==3,info=dataVert.{{1,0,0},{0,1,0},{0,0,-1}}];
Graphics3D[GraphicsComplex[info,Polygon[dataPoly]],AxesLabel->{"x","y","z"},Axes->True]
)

symmetry[0]

symmetry[1]

symmetry[2]

symmetry[3]