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4x5x5
Above:Solved
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The "biggest" cuboid in the range of N<=5.

After the first cuboids were presented it was easy to think about other cuboids that might be possible. It is surprising that the first one was built not earlier than 2005. After its presentation this specific variant was almost forgotten until Tanner Frisby built the second one in early 2010 and Ayi Liu the third in 2011.
The images used here are from the variants of Tanner and Liu.

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