Poo-Song Park, Regular polytopic distances,
Forum Geometricorum, 16 (2016) 227--232.

Abstract. Let M be an n-dimensional regular polytope of simplices, hypercubes, or orthoplexes and r be the circumscribed radius of M. If q^4 is the average of fourth powers of distances between a point and vertices of M and s^2 is the average of squares of those distances, then q^4 + (4(n+1)/n^2)r^4 = ((s^2 + (2/n)r^2)^2.

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