# Hypercube of Duads

This picture by Greg Egan shows a hypercube with all vertices except the bottom labelled by duads, that is, 2-element subsets of a 6-element set. There are 15 duads, while the hypercube has 16 vertices. In fact, we can think of this hypercube as a 4-dimensional vector space over the field with two elements, \(\mathbb{F}_2\).…