I have been thinking about the famous Klein bottle (above). To quote a limerick by Leo Moser:
A mathematician named Klein
Thought the Möbius band was divine.
Said he: “If you glue
The edges of two,
You’ll get a weird bottle like mine.”
Just for fun, here is a Game of Life glider on a Klein bottle. The top and bottom of the square are considered to be joined, so as to form a tube. The ends of the tube (vertical sides of the square) are also joined, but with a reversal of orientation (a manoeuvre not really possible in three dimensions). The glider changes colour as it changes orientation.
Video produced using the R