I uploaded file "Theory of hexaflexagons.pdf" to the Flexagon_Lovers files page. In this article I introduce the terminology that I use (where possible I stick...
Yaacov A welcome, elegant, addition to the literature on flexagons. Your splitting procedure is equivalent to what I call a main position link, where...
Les, I agree that it is very likely that other people developed similar ideas independently. In fact, I was too sure that's the case, and that's why I never...
Scott, 1) Regarding intuitive explanation of pat formula. A pat formula is a sequence of numbers corresponding to connecting edges. Each number means, in a...
All flexagons exist as enantiomorphic (mirror image) pairs. Some edge flexagons are twisted bands. A flexagon that is a twisted band must have an enantiomorph...
I've wondered for awhile if it's possible to flex between all foldings of a flexagon strip, and what flexes would be required if so. So I figured I'd try a...
Scott, A nice piece of work, and nice and clear explanations and diagrams on your new page! In my notation, the formulas of these states are (the first digit ...
Next I wanted to see what the slot flex adds to the mix. I started with a 5-sided hexaflexagon (from http://loki3.com/flex/braids.html, but numbered 1-5...
Yaacov, After I sent that message, I had also noticed there was at least one state that was isolated given my set of flexes. I believe I had found state L...
Yes, on point #3 I had overstated my case, so I'll rephrase it. It looks to me like face splitting preserves twist. You can generate all hexaflexagons (for...
Scott, Â I want to use this opportunity to clarify how to fold the strip based on the formula. The first step is to switch from the formula to the Tuckerman...
Yaacov, That takes a little while to digest. So if I understood that, state K is 1 2 (7 4 3 6 5) 8 (10 9) 11, yes? I assume that your observation that the...
Scott,  I just now found two emails from you that for some reason got to my spam folder. Now I will know to check the spam folder.  Yes, I know how many...
Scott, Â Yes, K is 1 2 (7 4 3 6 5) 8 (10 9) 11. Â Yes, you are right - the same changes by 2 and -2 are the reason why I considered these flexes (not...
Awhile back I had posted an 8-sided triangle pentaflexagon with the challenge of figuring out how to transform it from having sides 1 and 2 visible to having...
Nice result, Yaacov. It looks to me like this easily generalizes to other triangle flexagons beyond the hexaflexagon. The same logic applies whether you...
Scott, Â Other triangle flexagons are a fascinating new (for me) direction that I almost did not start to explore yet (but see below); I agree that it would...
After looking at various hexaflexagons, I would guess your conjecture in #3 is probably correct. The 11-leaf hexaflexagon I posted is the unique minimal...
Hmmm, I haven't seen anything where the goal was simply to decide if a flexagon can be folded from an arbitrary strip. The techniques I've tried have...
(This message replaces my previous message with the same subject that was not displayed properly. Also, I fixed several typos.) Â The algorithm described...
In continuation of the thread "Linear time algorithm that decides whether a strip can be folded to a flexagon", I folund a necessary and sufficient condition...
I've posted a new video showing some interesting flex sequences on the 10-sided isosceles triangle decaflexagon, including... * ..a flex I call the "flip flex"...
this group is definately not for beginners. it is for experienced. Pauline ... From: Scott Sherman loki3s@... Date: Sun, 22 Mar 2009 21:20:55 -0700 (PDT)...
Scott, Â A great video! That's the first time I folded a flexagon from non-equilateral triangles and did a 3-3-4 pinch flex. Looks like Tuckerman map still...
... Pauline I agree that some postings are for the experienced, but we do try to help newcomers. Have you any specific questions that you would like answered? ...
Certainly some of the posts can get pretty advanced, but there has actually been quite a mix. People are most likely to post new discoveries of course, which...
HOMAGE TO A PIED PUZZLER is now available through Amazon. Published by A K Peters, this book has a chapter by Jeff Rutzky and me on the hexa-dodeca-flexagon....
I've posted a new video showing some of the interesting flexes you can do on a silver octaflexagon, aka silverflexagon or 8-gon. It's folded from 45-45-90...
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