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In lugnet.build.schleim, David Eaton wrote:
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Of course, the thing that’s still missing is the 3x3x3 cube! We’ve discovered
how to make a 2x2x2, a 4x4x4, 5x5x5, and anything larger that’s an integer
multiple of studs... But no 3x3x3’s :(
The other thing that I haven’t seen tried is making non-integer multiple
cubes. Could you, say, make a cube whose edges were 3.5 long? Or 4 studs and
2 plates? I doubt anyone’s gonna get one that’s smaller than a 2-stud long
side, but if anyone can, I’d still love to see it!
DaveE
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hmmm. I have a suspicion that most non-integer cubes are impossible because of
the way the surfaces can be constructed.
Each side of a surface must be constructed out of I + 1/5 J plate units (I
and J integer) since we can only make them out of plates + half plate heights.
Since this makes a surface area of I^2 + 2/5 IJ + 1/25 J^2 it will only
work when J is a multiple of a power of sqrt(5). Since we cannot have an
irrational number of plates then J must be a multiple of 5 which brings us
back to an integer.
Tim
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 | | Re: Smallest cube ever!?
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| Of course, the thing that's still missing is the 3x3x3 cube! We've discovered how to make a 2x2x2, a 4x4x4, 5x5x5, and anything larger that's an integer multiple of studs... But no 3x3x3's :( The other thing that I haven't seen tried is making (...) (17 years ago, 22-Feb-07, to lugnet.build.schleim, FTX)
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