A Game of Four-folds, Part 2

One way to have all six arrangements of the quadrants for each four-fold card is to make a tetraflexagon for each card. Above are the two sides of a sheet that should be printed out by flipping it on the short edge, so that the upper right corner of the bottom image will end up behind the upper left corner of the top image. Then fold the tetraflexagon by the simple instructions found at the link below. Then you will have all six arrangements of the four-fold for the Four Elements! There are actually seven states for the tetraflexagon, six of which have a valid arrangement on just one side of it, and one that doesn’t have a valid arrangement on either side. Seems like a lot of work, though.

http://home.centurytel.net/cdefreese/foldables/folding_the_geometry_tetraflexagon.htm

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2 Responses to “A Game of Four-folds, Part 2”

1. Hayden White’s Metahistory | Equivalent eXchange Says:

[…] as with my problems with the synoptic table of Arthur M. Young, it would be nice to play the Game of Fourfolds to see if I can find better arguments for my synoptic claims, or to convince myself that the claims […]

2. A Game of Four-folds, Part 3 | Equivalent eXchange Says:

[…] another idea for the Game of Fourfolds, instead of using hexaflexagons. Since each fourfold can be permuted six ways, how about arranging […]

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