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Search: id:A071880
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| A071880 |
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Number of combinatorial types of n-dimensional parallelohedra. |
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+0
4
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OFFSET
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0,3
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COMMENT
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a(n) = number of topologically distinct shapes the Voronoi cell (or Vocell) of an n-dimensional lattice can have.
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REFERENCES
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J. H. Conway, The Sensual Quadratic Form.
P. Engel, The contraction types of parallelohedra in E^5, Acta Cryst. A 56 (2002), 491-496.
M. I. Stogrin, Regular Dirichlet-Voronoi partitions for the second triclinic group, Trudy Matematicheskogo Instituta imeni V. A. Steklova, 123 (1973) = Proceedings of the Steklov Institute of Mathematics, 123 (1973).
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EXAMPLE
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In 1 dimension: the Vocell is an interval (1 possible shape)
In 2 dimensions: a hexagon or rectangle (2 possible shapes)
In 3 dimensions: truncated octahedron, hexarhombic dodecahedron, rhombic dodecahedron, hexagonal prism, cuboid (5 possible shapes)
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CROSSREFS
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Cf. A071881, A071882.
Sequence in context: A004098 A005114 A081090 this_sequence A071882 A081482 A134475
Adjacent sequences: A071877 A071878 A071879 this_sequence A071881 A071882 A071883
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 10 2002
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EXTENSIONS
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Corrected by J. H. Conway, Dec 25 2003
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