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Permutohedron


The permutohedron is the n-dimensional generalization of the hexagon. The n-permutohedron is the convex hull of all permutations of the vector (x_1,x_2,...,x_(n+1)) in R^(n+1). The number of vertices is (n+1)!.


See also

Associahedron, Cyclohedron, Hexagon, Polytope

This entry contributed by Bryan Jacobs

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References

Hohlweg, C. and Lange, C. "Realizations of the Associahedron and Cyclohedron." 2 Dec 2005. http://arxiv.org/abs/math.CO/0510614.Postnikov, A. "Permutohedra, Associahedra, and Beyond." http://www-math.mit.edu/~apost/papers/permutohedron.pdf.Starck, M. "3D Representations." http://www.ac-noumea.nc/maths/amc/polyhedr/3D-img_.htm.

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Permutohedron

Cite this as:

Jacobs, Bryan. "Permutohedron." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Permutohedron.html

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