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Search: id:A119870
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| A119870 |
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Number of vertices of the root-n Waterman polyhedron. |
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9
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| 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
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OFFSET
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1,1
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COMMENT
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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]
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.
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CROSSREFS
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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: A075247 A040135 A004015 this_sequence A038332 A093763 A002548
Adjacent sequences: A119867 A119868 A119869 this_sequence A119871 A119872 A119873
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), May 26 2006
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