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Chains of Platonic Solids and a Tetrahedral Hoax
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| Organization: | Macalester College |
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Wolfram Technology Conference 2014
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Champaign, Illinois, USA
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For four of the five platonic solids it is easy to make a closed chain using copies of the solid that meet face to face. It was proved in 1957 that such a chain cannot be formed using regular tetrahedra. Using Mathematica to automate the search, we found a chain of regular tetrahedra that closes up except for a gap at the end, having size less than 10^-18 times the side length. This is well under the tolerance of a 3D printer, so one can make convincing physical models of the hoax chain. Such physical models will be shown. The outstanding unsolved problem is whether one can find tetrahedral chains having arbitrarily small gaps.
To download this presentation, go to:
ElgersmaWagonWTCTalk.nb
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Track: Math, Science, Engineering, Technology
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http://www.wolfram.com/events/technology-conference/2014
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