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Image links broken; now fixed.
Joseph O'Rourke
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Couldn't accomplish this in a comment to Rahul's #1, but here is a physical realization of my drawing with colored pencils. Compare:

alt text alt text

The pencils are in contact, but the lead inside could serve as lines in space without contacts. I don't know how to reconcile this with your quote from Whiteley...

Joseph O'Rourke
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  • 958