The revelation came as I was preparing to teach a lesson I call the "whirlwind tour" of folded books. I was looking particularly for structures that could be made from one piece of paper and printed on only one side. Ed Hutchins introduced me to these long ago, and they were an interest and specialty of his.
X Book. Pants Book. T-Cut, almost. Snake, almost. I stared at Snake again. Yes! I found that by wrapping one end around to the back and securing it there, the book feels more like a traditional codex and does not move as freely as an accordion. It is possible, and more than likely, in fact extremely likely, that someone figured this out long before I did since people who like to fold paper tend to discover these maneuvers on their own.
This close examination of the Snake book reminded me yet again how teaching can be a path to learning something new.