Flat origami shape foldable to reveal 5,6 or maybe 7 faces..

[Siganita]

In high school geometry class (many, many years ago) I remember making a two-dimensional folded shape - perhaps hexagonal, or octagonal, or some such - that, depending on how you folded it, revealed a different face. There were at least 4 faces (I remember because we decorated each face differently). Some faces were harder to get to than others.

I haven't been able to find what this is using google (for the better part of the day) because I don't know what to call such a thing - the closest I can think of is "puzzle" and "dynamic origami."

Based on this hazy description, can anyone lead me to a blueprint for how to make it?

Thanks so much!
Vivian

[origami_8]

Reminds me somehow on a flipper:
http://www.barf.cc/flipper.pdf
http://www.glynnorigami.co.uk/Flipper.htm

Or maybe a flexagon:
http://www.mathematische-basteleien.de/index.htm

[wolf]

Sounds like a flexagon.

Do a search on the O-list archives (http://origami.kvi.nl) - there was a fairly long discussion not too long ago about this curious beast.

[Siganita]

Yes!! Flexagon is absolutely what this was. Thank you guys so much. I can't wait to start making mine!

Is this a well-known shape? Is it considered origami? In mathematical terms, how would one describe this - even though "curious beast" seems, for my purposes, quite apt?

Best,
Vivian

[Siganita]

More advanced flexagram question

--How would one go about making, on one flexagram face, a face that sometimes is smiling, and in other forms apprears to be frowning?

I saw this on a website while still getting my bearings and did not bookmark it, but now I'm ready to make it and would love to get the smile/frown-face as one of the leaves of the flexagram.

These things are addictive.

Thanks so much,

Vivian

[denori]

David Mitchell has some good flexagon publications

http://www.mizushobai.freeserve.co.uk/publications.htm

[redgator12]

I actually came across this design on youtube, when a Catholic church down the road began handing out something called a Memory Cross, which is the design from Glynn's page, and I wanted to make one, but couldn't find the proper name. Thanks for both of the links

[HankSimon]

Vaguely related is a puzzle purse:
http://www.marthastewart.com/how-to/ant ... -valentine

Hexaflexagon: http://www.metacafe.com/watch/1174203/o ... aflexagon/
http://www.origaminut.com/178/hexaflexagon

Face Flexagon: http://www.mathemagic.org/MathsAndArt/flexagon.htm

- Hank Simon