  This paper precisely analyzes the wire density and required area in standard
layout styles for the hypercube. The most natural, regular layout of a
hypercube of N^2 nodes in the plane, in a N x N grid arrangement, uses
floor(2N/3)+1 horizontal wiring tracks for each row of nodes. (The number of
tracks per row can be reduced by 1 with a less regular design.) This paper also
gives a simple formula for the wire density at any cut position and a full
characterization of all places where the wire density is maximized (which does
not occur at the bisection).
