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The dodecahedron-icosahedron compound is a polyhedron compound consisting of a dodecahedron and its dual the icosahedron. In the compound, the dodecahedron and icosahedron ...

A number of attractive cube 10-compounds can be constructed. The first can be obtained by beginning with an initial cube and rotating it by an angle theta=sin^(-1)(sqrt(3/8)) ...

A magic cube is an n×n×n version of a magic square in which the n^2 rows, n^2 columns, n^2 pillars, and four space diagonals each sum to a single number M_3(n) known as the ...

A polyhedron compound is an arrangement of a number of interpenetrating polyhedra, either all the same or of several distinct types, usually having visually attractive ...

A semiperfect magic cube, sometimes also called an "Andrews cube" (Gardner 1976; Gardner 1988, p. 219) is a magic cube for which the cross section diagonals do not sum to the ...

A cube 13-compound can be constructed as the dual of the octahedron 13-compound. It will be implemented in a future version of the Wolfram Language as ...

A pandiagonal semiperfect magic cube is a semiperfect magic cube that remains semiperfect when any single orthogonal section is "restacked" cyclically so that the ordering of ...

A cube 35-compound can be constructed as the dual of the octahedron 35-compound. It will be implemented in a future version of the Wolfram Language as ...

What is the area of the largest square that can be inscribed on a unit cube (Trott 2004, p. 104)? The answer is 9/8, given by a square with vertices (1/4, 0, 0), (0, 1, 1/4), ...

Cube point picking is the three-dimensional case of hypercube point picking. The average distance from a point picked at random inside a unit cube to the center is given by ...