# Questions tagged [hypercube]

For questions involving cubes in higher dimensions or the hypercube graphs.

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### Number of hypercube unfoldings

While writing the code for this answer, I noticed that I not only could calculate the number of unfoldings of the $4$-cube, but also the number of the $n$-cube for more values of $n$. Basically, we ...
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### Cycles in the hyperoctahedral group (symmetries of the hypercube)

Let $B_n$ be the hyperoctahedral group (the isometries of the $n$-dimensional hypercube). Let $k <n$ and consider the action of $B_n$ on the $k$-dimensional faces of the hypercube. What can you ...
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### Hamiltonian cycle polytope for the hypercube graph

Let $Q_n$ denote the $n$ dimensional hypercube graph (i.e., graph formed from the vertices and edges of an n-dimensional hypercube). Denote the set of edges and vertices of $Q_n$ by $E_n$ and $V_n$ ...
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### Longest simple path through hypercube corners

This is a variation on a previously answered question, Longest path through hypercube corners. Here I am seeking the longest simple (non-self-intersecting) path through the unit hypercube's vertices, ...
Is the longest Hamiltonian path through the $2^d$ unit hypercube vertices known, where path length is measured by Euclidean distance in $\mathbb{R}^d$? The unit hypercube spans from $(0,0,\ldots,0)$ ...