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    Hexagonal Lattice

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    Description of lattice

    basis | (-1 | 1) | (0 | -1) Gram matrix | (2 | -1 -1 | 1)

    Lattice invariants

    dimension | 2 determinant | 3 minimal squared norm | 2 kissing number | 6

    Lattice-packing invariants

    packing radius | 1/sqrt(2)≈0.707107 covering radius | sqrt(2/3)≈0.816497 density | π/(2 sqrt(3))≈0.9069 center density | 1/(2 sqrt(3))≈0.288675 Hermite invariant | 2/sqrt(3)≈1.1547 thickness | (2 π)/(3 sqrt(3))≈1.2092 volume | sqrt(3)≈1.73205

    Quadratic form and theta series

    quadratic form | 2 x^2 - 2 x y + y^2 theta series (closed series) | (ϑ_3(0, e^(i π x))^3 + ϑ_3(π/3, e^(i π x))^3 + ϑ_3((2 π)/3, e^(i π x))^3)/(3 ϑ_3(0, e^(3 i π x)))

    More properties

    dual | dual root lattice | A_2

    Common properties

    integral | nonunimodular | odd

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