[math-fun] Kissing number question for an optimal cylinder

Define the "optimal cylinder" as the finite cylinder whose diameter equals its height.* Let C_0 := { (x,y,z) | x^2 + y^2 <= 1 and |z| <= 1 }. QUESTION: How many congruent copies of C_0 -- call them C_1,...,C_n -- can simultaneously touch C_0, subject to the RULE: Any two cylinders among C_0,...,C_n are allowed to overlap on their boundaries but must have disjoint interiors. (I don't know the answer, but for comparison's sake the largest n that I know works is listed far below. Perhaps this number can be proved maximum.) --Dan ________________________________________________________________________________________ * the cylinder with the most volume for a given surface area 20