Sure. Add an extra dimension with coordinate w to 3d space.
Then just rotate around the (x,y)-plane until z -> -z and w -> -w. Everything in the (x,y)-plane stays the same and z has been inverted.
Then just rotate around the (x,y)-plane until z -> -z and w -> -w. Everything in the (x,y)-plane stays the same and z has been inverted.