On 2016-04-07 16:51, rcs@xmission.com wrote:
I've seen this, maybe at a past G4G. Gosper?
Well, there's https://en.wikipedia.org/wiki/Prince_Rupert%27s_cube http://momath.org/home/math-monday-passing-a-cube-through-another-cube/ They've been called Ronayne's Cubes. http://www.gabrielnivasch.org/fun/hole-in-a-cube https://books.google.com/books?id=Aq5JAQAAMAAJ&pg=PA185&lpg=PA185&dq=cube+ca... https://books.google.com/books?id=ZZ9ZAAAAYAAJ&pg=PA185&lpg=PA185&dq=cube+ca... James Lee (shown with Jeannine Mosely, gosper.org/IMG_2161.JPG), who has been 3D printing since age 6, and I have been looking at this. The punctured cube is little more than a flimsy triangle. Passing one through another is not very impressive, so modelers usually leave one cube unpunctured. --rwg
There's a neglected part of this puzzle: Proving there's a path for the inner hypercube, through the outer hypercube. Confirming that the left over piece of the OH is connected, and that there's an actual tunnel through it. Perhaps showing that the IH can pass through the tunnel -- if it's not straight, maybe there are twists and turns?
We can check the 3D case with a model. But the higher dimensional margins are pretty skimpy, suggesting it might not be a cakewalk.
Rich
---------- Quoting Warren D Smith <warren.wds@gmail.com>:
actually, the 3D printers among us might want to construct the 3D case of this problem.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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