August 2015
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A possible solution is:
[0,0,0], [0,0,1], [0,0,2], [0,1,2], [0,1,1], [1,1,1], [1,1,2], [1,2,2], [2,2,2], [2,1,2],[2,0,2], [1,0,2], [1,0,1], [2,0,1], [2,0,0], [2,1,0], [2,2,0], [2,2,1], [1,2,1], [0,2,1],[0,2,0], [1,2,0], [1,1,0], [0,1,0], [0,0,0]
Thanks to Robert Gerbicz who pointed us to the cover of Peter Winkel's book Mathematical Mind-Benders (http://ecx.images-amazon.com/images/I/416HFW9R1AL._SX331_BO1,204,203,200_.jpg), which shows a solution; and to David Greer who sent us a great animation showing the solution: http://imgur.com/1zkpt5Y.
