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## For sharing a big Origami/Mathematics discovery and let people enjoy this discovery and finding more interesting Origami modle.

I would like to share an exciting Paper Tetrahedron Folding I found with you:
An A4(A or B are OK too) metric paper can be fold into
multiple (2N) interesting same shape and size tetrahedrons and the max 16 of
them can combine to a large shape with the same proportion. This
kind of tetrahedron named 2:root3 has 4 same isosceles triangle face,
with 2 same long edges and 4 same short edges. The most
changlenging one is to fold 16 same size tetrahedrons
with one A4 metric paper. I named 1/2， 1/4， 1/8 and 1/16 folding.
Than I have some questions and appreciate if you can give some advice:
1. How many kinds of model for the 1/2 size tetrahedrons existing ? I found 3 kinds.
2. How many kinds of model for the 1/4 size tetrahedrons existing ? I found 5 kinds.
3. How many kinds of model for the 1/8 size tetrahedrons existing ? I founds 15 kinds.

5. How many kinds of modle for the 1/16 size tetrahedrons existing ? I found 7 kinds now.

6 . I found a special method which can fold one modle of 2N (more > than 32)tetrahedrons. Is it other modle can be fold for the 2N numbers?

I thought it should need computer to solve problem number 6.
If it is possible,I would like to show the photoes of my multiple tetrahedrons
modle family. discovery to OrigamiUSA friends.

Sorry for my poor English.

I also give this question to Origami specialist Robert J Lang, he mailed me.

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## Closing Statement from Haisheng Liang

My talk show on Shanghai World Finace Center, Insights Talking, 19th Sep. 2012. http://video.sina.com.cn/v/b/86109686-1580841745.html

Inventor

Working as an engieer, Liang haisheng spares his own time in inventing for over 20 years. His inventions and artistic works won a lot of prizes in China. Especially for the paper folding, he created the exclusive ways of origami.
http://www.swfc-shanghai.com/event/201209swfcinsights/en.html

• #### Haisheng Liang

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Jul 4 2011: Lindsay thank you for your replied. I also thought my discovery has something relating to mathematics, design and construction, but I dont know the alink. Please let me know the link. Thank you!
• #### Lindsay Newland Bowker50+

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Jul 4 2011: Hello Haisheng

It is called Between the Folds available through Netflix as an instant download..do you have that?

http://www.pbs.org/independentlens/between-the-folds/

I hope you can get it because it will mean so much more to you with your experise and remarkable insights than it possibly could to me. I just loved it. And I love especially that math and science have learned so much about complex structural issues from origami.
• #### Lindsay Newland Bowker50+

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Jun 19 2011: I couldnt begin to speak to the esoterics of your particulars as you farmed the question but I did see a fascinating documentary on the matehematics of origami and how it is informing mathematics, design and construction. Do you happen to have alink to that? I'll find it and bring it here otherwise.

ould be fun to find one or two Tedster who can unapck this for the rest of us at your level.. but failing that, could we bring some background here to introduce poeple to the mgaic and mystery of origami?
• #### Haisheng Liang

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Jun 19 2011: A4 multiple tetrahedros Origami show at 2011 International Shanghai Sience and Art Exhibition. There are many children and old peoples are enjoyed trying fold the intersting tetrahedron in this video ,please have a look http://video.sina.com.cn/v/b/54463224-1580841745.html
• #### Haisheng Liang

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Jun 16 2011: People young and old like Tetrahedrons Origami Folding at ShangHai International Science and Art Exhibition, May 2011. Please look the video and you can see some tetrahedron Origami modles. Very intersting! http://you.video.sina.com.cn/m/1580841745
• #### Haisheng Liang

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Jun 15 2011: Dear Haisheng,

Thank you for the further pictures of your work. It
is surprising that there is so little origami in China, since China has
had paper longer than anyone else! But I imagine with the sweeping changes
in society there that they may well be more opportunity in the future for
Chinese origami artists, and you will be one of the first, it would
seem.

Unfortunately, Philip Shen died some years ago. He was
one of the pioneers of origami outside of Japan, active in the 1950s
through 1970s, and died 10-15 years ago. I had the privilege to meet him once.
Many of his origami creations are now considered classics.

Interestingly, many of his works were elegant 3-dimensional
polyhedral models, and so are somewhat reminiscent of your
tetrahedra structures. Not the same, but I think if I showed your work to someone
and said, "guess whose models these are," Philip Shen would be among

I would encourage you to get involved in some of the international origami
community; I think others would enjoy seeing your works, and you could
receive inspiration and ideas from some of what people are already doing.
Many of the international origami societies publish books and magazines
that you might enjoy reading (even with your current level of English,
which is quite good), and they could also serve as outlets for you to
publish your designs, should you so choose.

Of course, OrigamiUSA is a good place: http://www.origami-usa.org . The
British Origami Society is also good.

Best regards,

Robert