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