20 Jun
2018
20 Jun
'18
8:39 a.m.
A cuboid with sides 2^(1/3) to the powers of 0,1,2 can make a larger copy of itself. Delian Brick seems like a great name for it. It is a 2-reptile. https://math.stackexchange.com/questions/2822566/ Graphics3D[{Cuboid[{0, 0, 0}, {2^(0/3), 2^(1/3), 2^(2/3)}], Cuboid[{1, 0, 0}, {1 + 2^(0/3), 2^(1/3), 2^(2/3)}]}] 3D rep-tiles that are not derived from 2D rep-tiles are currently quite rare. I would not be surprised if this brick was known by the ancient greeks. Has anyone seen it before? --Ed Pegg Jr