During my first year of my PhD in mathematics, someone asked if I could knit a klein bottle, so I made this.

Here is the pattern I made up to do it. The gauge, yardage, needle size, yarn size, etc., is not important as it will just make a slightly different sized klein bottle.

The construction of this is made by making a long tube like object with a hole in it, and then connecting the ends together through the hole, so that it is a legitimate klein bottle.