# Diagonals in an n-cube

Geometry Level pending

Take a unit n-cube (an n dimensional analogue of a cube) in $$d$$ dimensions. The length of the longest segment connecting two points in the cube, or longest diagonal, is $$D$$. Let $$S$$ be the sum of all the distinct diagonals of length $$D$$. For this particular dimension, you are given that

$$\frac { { S }^{ 2 } }{ d } =64$$

What is $$d$$?

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