Drawing a perfect binary tree in three dimensions: Put the leaves evenly spaced on the outer sphere. One concentric shell in, the immediate parents; grandparents go another shell in.
The shell with 8 nodes is arranged a cube or twisted cube. The next one in is a tetrahedron. Can these two be nested in a nice symmetric way?
A binary tree grows faster than there is space, in any number of dimensions, resulting in a crowded depiction at the leaves. But three dimensions does better than two.
Inspired by single elimination tournament brackets.
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