Face of the Boolean hypercube
= Face of the Boolean hypercube
{title2=$Q_d$}
= Cube face
{synonym}
= Subcube
{synonym}
= Coordinate subcube
{synonym}
A face is obtained by fixing some coordinates of the <Boolean hypercube> and letting the remaining $d$ coordinates vary freely. It is isomorphic to $Q_d$. A two-dimensional face is a square with four vertices, and a face is contained in a <set family> when all its vertices belong to that family.