I'm going to say 6, octahedral arrangement. If one more sphere could fit, then more could fit, but only 12 unit spheres can fit around a unit sphere. --Ed Pegg Jr On Monday, June 1, 2020, 06:08:05 PM CDT, Dan Asimov <dasimov@earthlink.net> wrote: The kissing number in n dimensions is the maximum number K(n) of non-overlapping unit spheres that can be placed tangent to the one centered at the origin. Known kissing numbers: dimension kissing number —————————————————————————— 1 2 2 6 3 12 4 24 8 240 24 196560 No other kissing numbers are known. A related problem is to find the "anti-kissing number" in each dimension n: the smallest number A(n) of non-overlapping unit spheres in n-space, all tangent to the unit sphere centered at the origin, so that there's no room for any additional non-overlapping unit spheres tangent to the central one. It's obvious that A(1) = 2 and easy to show that A(2) = 4. Puzzle: What is A(3)? —Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun