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The Checkered Origami I-Triangle

Checkered Patterns

by Serhiy Grabarchuk

 

An Origami isosceles triangle.

 

Eight 2-unit-side checkered I-Triangles.
 
 
This is another triangular version of the Origami Checkerboard puzzle. Again, it uses an unusual sheet of paper -- this time in the form of a isosceles triangle colored just on one of its sides. It can be easy obtained from a standard Origami square.

In this page you can see eight, 2-unit-side patterns. Your challenge is to achieve every of the proposed patterns in the minimum of single "book" folds; see a sample. The final shape every time is a flat isosceles triangle; no matter what pattern will be at its back. Numbers next to the patterns indicate the minimal known numbers of folds necessary to perform them. Write us if you can improve any of these results.

All the solutions were found by Keiichiro Ishino.

Also, there are 455 3-unit-side patterns that can be obtained using an Origami isosceles triangle, and one day they will be posted as well. This exact number has been calculated by Keiichiro Ishino.

***
Even much more difficult challenges can be finding all the 4-unit-side checkered I-triangles and their minimal solutions. Recently, Keiichiro Ishino calculated that there are 187,343 substantially different 4-unit-side checkered I-triangles. Part of them have their solutions quite similar to the respective 3-unit-side checkered I-triangles described here, but it is obvious that most of them are rather difficult to be optimized.
 
 
Last Updated: October 14, 2008
Posted: September 4, 2005
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