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Let Y_n denote the graph with vertex set V(X_n), where X_n is the n-hypercube and two vertices are adjacent in Y_n iff they are at distance 1<=d<=2 in X_n. Y_n is not ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

For a connected bipartite graph G, the halved graph G^+ and G^- are the two connected components of the distance 2-graph of G. The following table summarizes some named ...

A hyperbolic version of the Euclidean cube.

A cube whose edge lengths are 1. The unit cube therefore has unit volume.

An n-fold multimagic cube is a magic cube that remains magic when each element is squared, cubed, etc., up to nth power. (Of course, when the elements of a cube are taken to ...

A tetramagic cube is a magic cube that remains magic when all its numbers are squared, cubed, and taken to the fourth power. Only two tetramagic cubes are known, and both ...

A trimagic cube is a magic cube that remains magic when all its numbers are both squared and cubed. Only two trimagic cubes are known. The first trimagic cube was found by C. ...

The folded n-cube graph, perhaps better termed "folded hypercube graph," is a graph obtained by merging vertices of the n-hypercube graph Q_n that are antipodal, i.e., lie at ...

A 6-piece polycube dissection of the 3×3 cube.