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Read about the Octa-Tetra club!
Exciting Math News!

A member of our HomeschoolingBOYS email group, Daniel Suttin of Uncle Dan's Algebra, shares about his project, the Octa-Tetra Club!


Uncle Dan "For many years, I have been interested in the way that "octahedrons" and "tetrahedrons" can be used as building blocks and did quite a few explorations. I even made several hundred "octas" and "tetras" out of wood and made a video record of everything I constructed, but I was disappointed to find that 5 "octas" do not come around to meet in a pentagonal structure; that the configuration is off by about 7 degrees. That meant that anything I had created involving pentagonal configurations was geometrically impossible. So I put the whole project aside for many years.



Then last year on the internet, I found an expert in this field, and asked him about this problem. He recommended that I try shortening the sides of some of the "octas" so that they are made of isosceles triangles rather that equilateral triangles.

Recently I found some time to work on this project and followed that suggestion. By trial and error, I arrived at the conclusion that if I took off about 2% from the sides of the triangles on one pyramidical half of the "octa", that I could achieve the desired result.

The other obstacle was how to assemble the "octas" and "tetras" and how to attach them together so that everything could be dismantled. After much thought and experimentation over the years, I finally discovered the simple paper clip. The piece shown in the following pictures is held together with a little over 9,000 paper clips; no glue was used. The project can be totally taken apart so that something else can be built. Even the individual "octas" and "tetras" can be dismantled and unfolded down flat for easy strorage.

I learned to slip the paper clips into position quite easily, and my 11-year-old daughter and 14-year-old son were able to do so as well. The times when I was attaching large sections that had been prefabricated were more difficult; I had to adapt my position to the project rather than the other way around. More than once I found myself lying flat on my back and holding a small flashlight between my teeth while I used both hands to slip a paper clip into position. But the fact that you are now looking at the pictures proves it can be done.

The pictures you see on this page are of a demonstration model which is desgned to show some of the potential of what can be built with an "OCTA-TETRA CONSTRUCTION SET". I purposely made changes as I worked my way through the project so as not to simply produce a totally symmetrical fascimile of one of the standard polyhedra, but rather to demonstate the capabilities of the "Octa-Tetra" system. What you are looking at is just one example of an infinite number of projects that can be built within the OCTA-TETRA world.

Of course everything I did was cut and scored by hand, a task I would not wish upon anyone, but I am looking into getting a little hand powered machine that can cut and score my templates for me. I am planning on putting together an instruction booklet with photos that I can send out for FREE by e-mail attachments. Then if I can find enough people who are interested, we could form an "OCTA-TETRA" Club where folks could send me pictures of their creations and I could send them out to all members in an e-mail newsletter. And people could order the pre-cut and pre-scored pieces from me which I would make available for just enough above my costs to cover my investment in the machine, the custom-made dies, and the card stock, shipping, etc. etc."

Uncle Dan would like to hear what you think of this new project, and if you, or anyone you know, would be interested in joining an "OCTA-TETRA CONSTRUCTON" Club. Please visit the Octa-Tetra Page or Email Uncle Dan and let him know!















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