Last week, YouTube's resident mathematical mind-blower, Vi Hart, introduced many of us to the topological wonder that is the hexaflexagon. If you haven't seen it yet, get your life in order and go check it out. In fact, even if you have seen it, go ahead and watch it again. Then reconvene with us here for round two of hexaflexagons!

Back with us? Excellent — then you know that last week, Hart dubbed October "The Month of the Flexagon," and we told you we'd keep you posted on any future flexagon flicks. This is us making good on our word. In this newly released video, Hart takes us on an historical journey through some of the hexaflexagon's more subtle properties. For instance: why is it that different faces of the hexaflexagon can be reached by passing through some surfaces and not others, and what is the quickest way to get from one side of the multi-faceted flexagon to any of its many other sides?

And to all the fellow physics nerds scratching their heads over the term "Feynman Diagram": no, Hart is not referring to the physicist's famed representations of subatomic particles. As it turns out, the term "Feynman Diagram" was first used to describe the behavior of crazy scrap-paper topology projects. Go figure.

The Month of the Flexagon continues! Don't forget to observe the annual Worldwide Celebration of Mind on Oct. 21st, in honor of the flexagon, Martin Gardner and his Mathematical Games column. You can read Gardner's column on hexaflexagons, first published in 1956, here.

[Vi Hart]