How to make a Klein Bottle in N easy steps

Hey kids! Make a hole-filled 3-dimensional representation of a 4-dimensional non-orientable manifold by following these easy steps!

1. Throw a pair of toruses. You will find Klein Bottle assembly easier than I did if you make the diameter of the holes about the same size as the diameter of the cross-sections. Remember to cut the toruses off the bat and to poke a small hole in them so air can escape while they're drying.

2. Because it's a lovely, sunny, spring-like day, put the toruses outside to dry. Run out of patience after an hour or two and trim them while they're still too wet.

3. Resolve to be more patient: you will let the toruses dry until they're soft leather hard. Fail to observe, when you were trimming them, that you accidentally filled in the pin holes that the air was supposed to escape from.

4. Check on the toruses later and discover they are beyond soft leather hard. Curse.

5. Decide which torus's cross section is more likely to fit better into the other torus's hole, and cut a segment out of the former (~1/8 of the total circumference). When you insert the knife and hear the air gushing out of the closed form, be grateful that neither torus ruptured while drying.

6. Moisten the outside of the cut torus to soften it up. Because you let it get too dry to have the right plasticity, it will split open as you stretch and reshape it. Curse.

7. Observe that it's too late in the day to throw another pair of toruses. Try to reseal the split, then decide to make lemonade out of lemons: the split gives you a way to widen one end so it fits into the second torus's too-large hole (see #1 above). Success is 90% attitude. You are the boss of the clay.

8. A little algebra yields Force them thangs together. Slide the unsplit end of the first torus through the donut hole of the second until the split end reaches the hole. Score, slip, attach. Patch the gaping split with clay previously cut from the first torus. Trim the other end of the first torus to fit the side of the second torus; cut a corresponding hole in the second torus; score, slip, attach, patch, smooth, etc. Voila: you have made a 3-D representation of a Klein Bottle.

9. Observe that all that moistening, smashing, tilting, patching, and mashing has seriously dented your Klein Bottle. From here on out, rest it on bubble pack or foam.

10. You wisely understand that aesthetic defects like dents can be hidden by more prominent surface alterations. Enjoy feeding your obsession with holes.

11. Realize it's kind of tricky fitting your hole-cutting tool into all the nooks and crannies. Plan to make the toruses more bagel-like next time.

12. Note that cutting from the outside of the inside to the inside of the outside yields better looking holes than cutting in the other direction.

13. Smooth out the surface dings by gently wiping the whole thing with a damp sponge. Appreciate the silkiness and forgiving nature of the Loafer's Glory clay body.

14. Because you are a responsible potter, as you contemplate how you will fire your Klein Bottle, also ponder how and when you will get the little bits of clay goobers (the detritus of punched holes) out of it. I'm 99% certain that no one wants to eat a handful of m&ms with vitrified clay goobers mixed in.