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Cube duplication, also called the Delian problem, is one of the geometric problems of antiquity which asks, given the length of an edge of a cube, that a second cube be ...

Attractive compounds can be constructed from the cube 3-compounds and their octahedron 3-compound duals. One is illustrated above. This compound will be implemented in a ...

The cube-octahedron compound is a polyhedron compound composed of a cube and its dual polyhedron, the octahedron. It is implemented in the Wolfram Language as ...

The 12-vertex graph consisting of a cube in which two opposite faces (say, top and bottom) have edges drawn across them which connect the centers of opposite sides of the ...

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 ...

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 ...

The augmented truncated tetrahedron is Johnson solid J_(66) constructed by affixing a square cupola to one of the octagonal faces of a truncated cube such that the cupola's ...

The cube-octahedron 5-compound is a polyhedron compound of the cube 5-compound and its dual, the octahedron 5-compound. It will be implemented in a future version of the ...

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 solid dissection puzzle invented by Piet Hein during a lecture on Quantum Mechanics by Werner Heisenberg. There are seven soma pieces composed of all the irregular ...