hi all, when building a 3D set of points using a simple rule, I accidentally found a subset that seems to approach icosahedral symmetry. Why 'approach' ? because all points in my set are rationals, and those can never be icosahedral since they lack the necessary Sqrt[5] irrationality. The procedure is simple enough: start from the tetrahedron (zeroth generation) {0, 0, 0}, {1, 1, 0}, {1, 0, 1}, {0, 1, 1} and on each triangular face, add the point to form the fourth vertex of a new tetrahedron: {{4/3, -1/3, -1/3}, {-1/3, -1/3, 4/3}, {-1/3, 4/3, -1/3}, {4/3, 4/3, 4/3}} The second generation is: {{5/9, 4/9, -11/9}, {4/9, -11/9, 5/9}, {-11/9, 5/9, 4/9}, {5/9, 20/9, 5/9}, {20/9, 4/9, 4/9}, {4/9, 4/9, 20/9}, {4/9, 20/9, 4/9}, {5/9, 5/9, 20/9}, {5/9, -11/9, 4/9}, {-11/9, 4/9, 5/9}, {4/9, 5/9, -11/9}, {20/9, 5/9, 5/9}} and so on, with the n-th generation having denominators 3^n, and the number of points tripling each generation. The quasi-icosahedron becomes apparent when selecting all points at Sqrt[2] from the origin. The zeroth generation provides 3 such, the first generation also, the second provides six, and the k-th generation provides 3*2^k of them. Apart from plotting and admiring their inane beauty, I didn't succeed in understanding where the underlying connection to their pseudo-icosahedral grouping comes from. You got to plot them to believe it. squarely yours, Wouter.