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Delaunay and voronoi polytopes of the root lattice E 7 and of the dual lattice E*7

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Abstract

We give a detailed geometrically clear description of all faces of the Delaunay and Voronoi polytopes of the root lattice E 7 and the dual lattice E*7. Here three uniform polytopes related to the Coxeter-Dynkin diagram of the Lie algebra E 7 play a special role. These are the Gosset polytope P Gos = 321, which is a Delaunay polytope, the contact polytope 231 (both for the lattice E 7), and the Voronoi polytope P V(E*7) = 132 of the dual lattice E*7. This paper can be considered as an illustration of the methods for studying Delaunay and Voronoi polytopes.

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Authors and Affiliations

  1. Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418, Russia

    V. P. Grishukhin

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  1. V. P. Grishukhin
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Correspondence to V. P. Grishukhin.

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Original Russian Text © V.P. Grishukhin, 2011, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Vol. 275, pp. 68–86.

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Grishukhin, V.P. Delaunay and voronoi polytopes of the root lattice E 7 and of the dual lattice E*7 . Proc. Steklov Inst. Math. 275, 60–77 (2011). https://doi.org/10.1134/S0081543811080049

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