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Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

The polyhedron compound of the truncated cube and its dual, the small triakis octahedron. The compound can be constructed from a truncated cube of unit edge length by ...

Since (2a)/(a+b)=(2ab)/((a+b)b), (1) it follows that a/((a+b)/2)=((2ab)/(a+b))/b, (2) so a/A=H/b, (3) where A and H are the arithmetic mean and harmonic mean of a and b. This ...

A number n for which the product of divisors is equal to n^2. The first few are 1, 6, 8, 10, 14, 15, 21, 22, ... (OEIS A007422).

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 magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a ...

A three-dimensional data set consisting of stacked two-dimensional data slices as a function of a third coordinate.

The 14-faced Archimedean solid with faces 8{3}+6{8}. It is also the uniform polyhedron with Maeder index 9 (Maeder 1997), Wenninger index 8 (Wenninger 1989), Coxeter index 21 ...

A method for constructing magic squares of singly even order n>=6.