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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 average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

A chamfered cube, also inaccurately called a truncated rhombic dodecahedron or more accurately called a tetratruncated rhombic dodecahedron, is a polyhedron obtained by ...

The dodecahedron-small triambic icosahedron compound is a stellated form of a truncated icosahedron, but a different truncation than in the truncated icosahedron Archimedean ...

An n-fold multimagic cube is a magic cube that remains magic when each element is squared, cubed, etc., up to nth power. (Of course, when the elements of a cube are taken to ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...

A tetramagic cube is a magic cube that remains magic when all its numbers are squared, cubed, and taken to the fourth power. Only two tetramagic cubes are known, and both ...

A figurate number of the form, CCub_n=n^3+(n-1)^3=(2n-1)(n^2-n+1). The first few are 1, 9, 35, 91, 189, 341, ... (OEIS A005898). The generating function for the centered cube ...

The mean triangle area of a triangle picked at random inside a unit cube is A^_=0.15107+/-0.00003, with variance var(A)=0.008426+/-0.000004. The distribution of areas, ...

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