If you map both x to -x and y to -y (in addition to mapping z to -z), then you still get a reversed (chiral) image. From the pictures, it looks like it maps x t

If you map both x to -x and y to -y (in addition to mapping z to -z), then you still get a reversed (chiral) image. From the pictures, it looks like it maps x to -x, but y is kept the same.