The torus or Klein bottle shown below is a 2-dimensional space. What does the ladybug see when she looks around her world? When she looks to the north, she sees herself as well as the three other things in her world. When she looks to the east, south or west, she again sees herself and the other three objects. She has the illusion of seeing infinitely many copies of each object.
Use the popup menu (below right) to change the picture from the fundamental domain view to the tiling view. Grab an object and move it around. Then switch from torus to Klein bottle, and again try moving an object around. What's different in the Klein bottle?