Hexaflexagon

I paid a king’s ransom for eight king’s heads so I could post two cards to arrive at different places before Sunday.


Mr Pandammonium sent me a link to a video yesterday. Since then, I have become obsessed with hexaflexagons.

You might think they’re passé or you might never have heard of them. If you’re in the former camp, I don’t care. If you’re in the latter camp, watch Vihart’s hexaflexagon series on YouTube. And don’t think I won’t be making those burritos, because I will.

I got to grips with the trihexaflexagon, so named because it has six sides and three faces.

I tried to get my head round the hexahexaflexagon, so named because it has six sides and six faces. My brain is hurting. It seems like there are six sides, but each of three of the sides are different. The Feynman diagrams in the photo show this quite clearly. Don’t they?

The top Feynman diagram represents the transitions; the bottom Feynman diagram represents the transitions of you flip it over (as with a pancake, but not in a hot pan).

Taking the top one, face 1 (with face 3 on the reverse) goes to face 2 (with face 1 on the reverse); face 2(1) goes to 3(2). That’s the black/grey loop. In the pink loop, face 1(3) goes to 6(1), which goes to 3(6), which goes back to 1(3).

Notice that face 3 occurs in each of these loops, but that it has different faces on the reverse. These are different face 3s.

I used a lot of marker pens, both permanent and dry wipe, to come to this understanding of the hexahexaflexagon. I had to make two hexahexaflexagons because I messed up the first one. I had to use a whiteboard because I kept messing up on paper.

Next stop, the tetraflexagon.