The Mandelbear's Musings

The adventure starts with this post by jenkitty containing directions for knitting a Klein Bottle hat, ganked from this page on one-sided surfaces.

That, of course, immediately led me to remember this hat at the Acme Klein Bottle online store. Somewhere around here I recalled my friend Ted's amusing account of trying to commission a Klein Bottle from a glassblower in Germany. (He eventually succeeded.)

A few more links lead to the geometric topology section of the Geometry Junkyard, and an online book called Math That Makes You Go Wow: A Multi-Disciplinary Exploration of Non-Orientable Surfaces.

Finally, combining non-orientable surfaces with another of jenkitty's interests, I tracked down this appendix to The Ultimate Science Fiction Poetry Guide, which contained the correct text and attribution for a limerick I remembered reading in the December 1968 issue of Martin Gardner's Mathematical Games column of Scientific American: it's by the late science fiction author Cyril Kornbluth:

 A burleycue dancer, a pip
 Named Virginia, could peel in a zip;
     But she read science fiction
     And died of constriction
 Attempting a Mobius strip.

(The icon, BTW, is a 120-cell ganked from this Wikipedia article