Video on Myriahedral Projections
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http://www.youtube.com/watch?v=b1xXTi1nFCo
This video on Myriahedral Projections is a great illustration of how projections work in general, but the cuts it makes are fantastic. Myriahedral Projections have many sides, but are (almost) conformal and conserve areas well. This video is entertaining for any crowd.
Recent Paper on Myriahedral Projections here: http://www.win.tue.nl/~vanwijk/myriahedral/CAJ103.pdf