| context | $n\in\mathbb N, n\ge 1$ |
| definiendum | $ Q_n\equiv\langle V,E \rangle $ |
| postulate | $ V=\{0,1\}^n $ |
| for all | $ v,w\in V $ |
| range | $ k\in\mathbb N, 1\le k\ne n $ |
| postulate | $ \{v,w\}\in E \leftrightarrow \exists! k.\ \pi_k(v)\neq \pi_k(w) $ |
The n-cube $Q_n$ is the graph with vertices being n-tuples which are connected exactly if they differ by one coordinate.
$V(Q_2)=\{\langle 0,0\rangle,\langle 0,1\rangle,\langle 1,0\rangle,\langle 1,1\rangle\}$
$E(Q_2)=\{\{\langle 0,0\rangle,\langle 0,1\rangle\},\{\langle 0,0\rangle,\langle 1,0\rangle\},\{\langle 0,1\rangle,\langle 1,1\rangle\},\{\langle 1,0\rangle,\langle 1,1\rangle\}\}$
… that's a square.