Question 54
Let $n$ be a positive integer. A Steiner tree associated with a finite set $S$ of points in the Euclidean $n$-space is a finite collection $T$ of straight-line segments in that space such that any two points in $S$ are joined by a unique path in $T$; its length is the sum of the segment lengths. Show that there exists a Steiner tree of length $1 + (2^{n-1} - 1)\sqrt{3}$ associated with the vertex set of a unit $n$-cube.
