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A119870 Number of vertices of the root-n Waterman polyhedron. 9
12, 6, 24, 12, 24, 32, 48, 54, 36, 24, 48, 24, 72, 72, 48, 60, 48, 54, 72, 72, 72, 72, 48, 56, 132, 96, 120, 96, 72, 72, 96, 102, 96, 96, 120, 84, 120, 144, 96, 72, 120, 72, 168, 168, 120, 120, 144, 168, 108, 126, 168, 72, 144, 152, 144, 144, 192, 120, 144, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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]

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.

LINKS

Table of n, a(n) for n=1..60.

CROSSREFS

Cf. A119870, A119875 [vertices of void-centered Waterman polyhedron].

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.

Sequence in context: A173853 A040135 A004015 * A234516 A177690 A038332

Adjacent sequences:  A119867 A119868 A119869 * A119871 A119872 A119873

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, May 26 2006

STATUS

approved

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Last modified December 11 00:29 EST 2016. Contains 279033 sequences.