... M. Tagami: On optimal sets in Musin’s paper The kissingnumber in four dimensions” in the Proceedings of the COE Workshop on Sphere Packings,November 1-5, 2004, in Fukuoka Japan). Now this ... thatthree other points yi,yj,yqlie inside the hemisphere H+bounded by Ω2. Let ΩAnnals of Mathematics The kissing number in four dimensions By Oleg R. Musin THE KISSING NUMBER ... ,θm) the efficient function. Clearly, iff ∈ Φ∗(z), then the efficient function is a monotone decreasing function in the interval [0,θ0] for any variable θk. THE KISSING NUMBER IN FOUR DIMENSIONS135-B....