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How Many Pentacubes?
“Uncle Bob”

In the figure below, you see isometric sketches of the cube and 5 of the 8 distinct solids that can be made using four of them – the tetracubes. All cubes must all be joined to at least one other along full faces.

1. On isometric grid paper, sketch the other 3 tetracubes. (Hints: right- and left-handed figures are considered different, and the other solids might not be contained between parallel planes one unit apart, as the lower right solid illustrates).

2. Build and sketch all the possible pentacubes (solids made of 5 cubes joined at full faces). Be sure to explain how you know that you have found them all, and how you made sure you didn't count the same solid twice.

Solution

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