Impossible Frames
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Each of the four corners for a frame made of four beams can be drawn in four different ways in 2D. There are 256 such frames, but most of them are impossible to construct physically as continuous 3D frames.
Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA
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"Impossible Frames"
http://demonstrations.wolfram.com/ImpossibleFrames/
Wolfram Demonstrations Project
Published: March 7 2011