|
%I #5 Mar 31 2012 10:29:09
%S 12,6,24,12,24,32,48,54,36,24,48,24,72,72,48,60,48,54,72,72,72,72,48,
%T 56,132,96,120,96,72,72,96,102,96,96,120,84,120,144,96,72,120,72,168,
%U 168,120,120,144,168,108,126,168,72,144,152,144,144,192,120,144,144
%N Number of vertices of the root-n Waterman polyhedron.
%C The root-n Waterman polyhedron is the convex hull of the intersection of a closed ball of radius sqrt(2*n) with the lattice of sphere-center points of a cubic close packing. [Probably the f.c.c. lattice is intended here. - _N. J. A. Sloane_, Aug 09 2006]
%C The basic sphere center series of Waterman polyhedra is obtained by choosing a sphere center as the center of the closed ball. Other choices are possible. An example is given in A119874 ... A119878. For n in A055039 no lattice points are hit; the corresponding polyhedra are the same as for n-1.
%Y Cf. A119870, A119875 [vertices of void-centered Waterman polyhedron].
%Y Cf. A055039 [missing polyhedra]. Properties of Waterman polyhedra: A119870 [vertices], A119871 [faces], A119872 [edges], A119873 [volume]. Waterman polyhedra with different center: A119874, A119875, A119876, A119877, A119878.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, May 26 2006
|
