The Outercoarseness of the n-cube.

Guy and Nowakowski showed that the outercoarseness of the n-cube was, for sufficiently large n, at least 0.96 of its maximum possible value, n.2(n-4). Here we give some exact results, including that the maximum is attained for all n >= 24. We construct explicit partitions of the edges of the cube attaining this maximum in which each part is a tepee, namely, the three-cube with a vertex and a non-incident edge deleted. Its vertices and those of the cube are given binary labels, which we often write in octal (base 8) or hexadecimal (base 16) notation.