%I A119870
%S A119870 12,6,24,12,24,32,48,54,36,24,48,24,72,72,48,60,48,54,72,72,72,72,48,56,
%T A119870 132,96,120,96,72,72,96,102,96,96,120,84,120,144,96,72,120,72,168,168,
%U A119870 120,120,144,168,108,126,168,72,144,152,144,144,192,120,144,144
%N A119870 Number of vertices of the root-n Waterman polyhedron.
%C A119870 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 (njas(AT)research.att.com), Aug 
               09 2006]
%C A119870 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 A119870 Cf. A119870, A119875 [vertices of void-centered Waterman polyhedron].
%Y A119870 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.
%Y A119870 Sequence in context: A075247 A040135 A004015 this_sequence A038332 A093763 
               A002548
%Y A119870 Adjacent sequences: A119867 A119868 A119869 this_sequence A119871 A119872 
               A119873
%K A119870 nonn
%O A119870 1,1
%A A119870 Hugo Pfoertner (hugo(AT)pfoertner.org), May 26 2006