Chaitanya's Random Pages

February 13, 2012

Decomposition of a 3x3x3 cube

Filed under: mathematics — ckrao @ 9:14 pm

Here is a decomposition of a 3 by 3 by 3 cube that I learnt recently: it can be divided into six 2x2x1 blocks and three unit cubes. The following diagram attempts to show this in layers, where the unit cubes are in red and the 2x2x1 blocks are each shown in a different colour.

A question for the interested reader: do all such decompositions necessarily have the unit cubes appearing along a diagonal of the 3x3x3 cube?

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