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There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

The average number of regions into which n randomly chosen planes divide a cube is N^_(n)=1/(324)(2n+23)n(n-1)pi+n+1 (Finch 2003, p. 482). The maximum number of regions is ...

A first compound of 20 octahedra can be constructed from the vertices of icositruncated dodecadodecahedron uniform polyhedron and a second from the vertices of the great ...

A cube can be divided into n subcubes for only n=1, 8, 15, 20, 22, 27, 29, 34, 36, 38, 39, 41, 43, 45, 46, and n>=48 (OEIS A014544; Hadwiger 1946; Scott 1947; Gardner 1992, ...

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 Fibonacci cube graph of order n is a graph on F_(n+2) vertices, where F_n is a Fibonacci number, labeled by the Zeckendorf representations of the numbers 0 to F_(n+2)-1 ...

A polyhedron compound of the great icosahedron and its dual great stellated dodecahedron most easily constructed by adding the polyhedron vertices of the former to the latter.

The cube of a graph is defined as its third graph power.

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 ...