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The Császár polyhedron is a polyhedron that is topologically equivalent to a torus which was discovered in the late 1940s by Ákos Császár (Gardner 1975). It has 7 polyhedron ...

Ueberhuber (1997, p. 71) and Krommer and Ueberhuber (1998, pp. 49 and 155-165) use the word "quadrature" to mean numerical computation of a univariate integral, and ...

There are a number of attractive cube 20-compounds that can be constructed by taking the duals of the octahedra in the two octahedron 20-compounds. The second of these was ...

There are a number of attractive cube 25-compounds. One can be constructed from the vertices of the second dodecahedron 6-compound (or second tetrahedron 50-compound) and ...

Given the above figure (without looking at the figure below!), determine how to disengage the two slotted cube halves without cutting, breaking, or distorting. One possible ...

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 ...

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), ...

Given four points chosen at random inside a unit cube, the average volume of the tetrahedron determined by these points is given by ...

A number is said to be cubefree if its prime factorization contains no tripled factors. All primes are therefore trivially cubefree. The cubefree numbers are 1, 2, 3, 4, 5, ...

The cubefree part is that part of a positive integer left after all cubic factors are divided out. For example, the cubefree part of 24=2^3·3 is 3. For n=1, 2, ..., the first ...