The Thrice Three-Fold Flexagon

Updated 7 April 2009.

To view the document click on the following link thrice-three-fold-31

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2 Responses to “The Thrice Three-Fold Flexagon”

  1. ralph jones Says:

    Hello Les Pook,

    As a result of your “Festive Flexagon”, I have developed an interest with flexagons. That seemed pretty straight forward. [The references to figures 10.55 and 10.57 have an extra “5”.]

    More interesting is the “Thrice Three-Fold Flexagon”.
    [Figure 2(a) doesn’t match with 2(b,c,d).]

    The flap flex Tuckerman traverse, and the pocket flexes to the hexagon were trivial. The pyramids and three flap pseudo 4-cycle was easy. The twist flex to the trapezium and rhombus positions was not difficult. And I was able to mark the triangle position so I could easily return to it.

    I have not been able to get/understand the asymmetric 4-fold pinch flex. Using the net from figure 12, I got the positions in 11(d), 11(c) and 11(b) [which is mislabeled 11(c) also, and you have what appears to be a “3” on the leftmost leaf where I have a “1”].
    But so far I cannot get to, nor back to, 11(a).
    Perhaps you used a different net for the picture in 11(a)?
    Any help on this will be appreciated.

    Are faces 3,4 accessible with some sort of flex?

    Thank you, and have a great day.
    Ralph Jones

  2. Les Pook Says:

    Ralph Jones

    Thanks for your comments. My responses are.

    In Figures 2 and 11 I didn’t try to match the numbers so I’m not surprised that they don’t match. Posing flexagons to photograph them is quite tricky due to minor imperfections, and it is sometimes necessary to flex to a different version of the same position.

    All of the photographs of the Thrice Three-Fold Flexagon are of the same card model so it is possible to get to all of the positions illustrated, but not necessarily directly.

    It is easier to carry out the asymmetric 4-fold pinch flex without actually passing through Figure 11(a). It was some time before I realised that this position was possible, and included it because of its symmetry.

    I don’t think it is possible to get to faces 3 and 4.

    I don’t fully understand the Thrice Three-Fold Flexagon. A fellow member of the Flexagon Lovers Group described it as ‘challenging’. I rewrote its description for ‘Serious Fun with Flexagons’ to try and make it easier to follow. My rewrite includes the comment that face numbers in all four nets are the same, but face letters differ.

    Happy flexing

    Les Pook

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