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Topic: What looks like a circle from either side and the top but isnt?

Why, the intersection of three orthogonal cylinders of course! smile (Otherwise known as a Steinmetz solid)

Firstly - Full credit for the Openscad program, and my awareness of this, goes to Ed Nisley from his blog over at http://softsolder.com/ (If you are into hacking in the true sense - gadgets, cnc's, electronics, home repairs, just damn interesting 'stuff', then check out his blog! his not selling nunthin' smile )

Having a moment between 'stuff', I felt like having something novel to fiddle with that was also educational wink Anyway, over at softsolder I recalled an article ( here - Ed's moved onto a very nicely setup M2 now, so don't hold the thing-o-matic against him wink ) that provided a nice model that demonstrates the limitations of describing 3D objects in a traditional "plan"/"elevation" sense . This is why its difficult to just 'scan' something - such as a photo - and reliably recreate a 3D model.

Anyway, If you take 3 cylinders and intersect them like the image below:
http://mathworld.wolfram.com/images/eps-gif/SteinmetzCylinders3_400.gif
you end up with a shape that you can view;
as a circle from the top:
https://lh4.googleusercontent.com/-e5tY8fLN_JI/UwIQeXrnDvI/AAAAAAAAKWE/xYtYQs3rhmo/w690-h692-no/top_orth.jpg
plan and side views
https://lh6.googleusercontent.com/-p9lHqW8Xp78/UwIQdd0P4tI/AAAAAAAAKV8/nE-YgTSe6nk/w690-h692-no/left_orth.jpg
https://lh6.googleusercontent.com/-uKUrmhQgSto/UwIQdTl5xEI/AAAAAAAAKV4/nBRXvZZEZCw/w690-h692-no/right_orth.jpg

But something else entirely when viewed from diagonal;
https://lh6.googleusercontent.com/-bg-KOedeU64/UwIQdb5V4oI/AAAAAAAAKWI/vmyz6BO5y_E/w690-h692-no/diagonal_orth.jpg


It will roll like a cylinder on a desk or down a hill, and doesn't feel like a hexagon when rolled in your hand.

Attached is the STL I printed - use .25mm, 25% infill, 2 perimeter, but you can produce your own using the openscad code on Ed's blog. It also uses his filament pin alignment system - use a 1.75mm piece of filament (its 2.9mm in his openscad code) cut to about 10mm to hold the sides together, using some glue to permanently bond it - although the pins in my piece hold it together fine.
https://lh6.googleusercontent.com/-kRw44P1lSRM/UwISEgfegyI/AAAAAAAAKXY/WHEM8CLvkTU/w1083-h747-no/20140218_004237.jpg
https://lh3.googleusercontent.com/-rZJgSKZD-nQ/UwIR3vSR9DI/AAAAAAAAKXo/hsN4n-ZCk-g/w1083-h730-no/20140218_004217.jpg

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orthcyl.stl 224.03 kb, 10 downloads since 2014-02-17 

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Re: What looks like a circle from either side and the top but isnt?

Very cool.  I'm going to print one for my daughter to take to geometry class.

3 (edited by adrian 2014-02-22 01:47:51)

Re: What looks like a circle from either side and the top but isnt?

I had great fun breaking an (construction) architects mind for a few hours yesterday with this.... was most enjoyable

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Re: What looks like a circle from either side and the top but isnt?

Thanks Adrian. Totally going to print this out.