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    Hexagonal Close Packing

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    Lattice invariants

    dimension | 3 minimal squared norm | 1 smallest vectors | (1 | 0 | 0) | (-1 | 0 | 0) | (1/2 | sqrt(3)/2 | 0) | (1/2 | -sqrt(3)/2 | 0) | (-1/2 | sqrt(3)/2 | 0) | (-1/2 | -sqrt(3)/2 | 0) | (0 | -1/sqrt(3) | sqrt(2/3)) | (0 | -1/sqrt(3) | -sqrt(2/3)) | (1/2 | 1/(2 sqrt(3)) | sqrt(2/3)) | (1/2 | 1/(2 sqrt(3)) | -sqrt(2/3)) | (-1/2 | 1/(2 sqrt(3)) | sqrt(2/3)) | (-1/2 | 1/(2 sqrt(3)) | -sqrt(2/3)) kissing number | 12

    Lattice-packing invariants

    packing radius | 1/2 = 0.5 covering radius | 1/sqrt(2)≈0.707107 density | π/(3 sqrt(2))≈0.74048 center density | 1/(4 sqrt(2))≈0.176777 volume | 1/sqrt(2)≈0.707107

    Quadratic form and theta series

    theta series (closed series) | 1/2 ϑ_2(0, e^((8 i π x)/3)) (ϑ_2(0, e^((2 i π x)/3)) ϑ_2(0, e^(2 i π x)) + ϑ_3(0, e^((2 i π x)/3)) ϑ_3(0, e^(2 i π x))) + (ϑ_3(0, e^((8 i π x)/3)) - 1/2 ϑ_2(0, e^((8 i π x)/3))) (ϑ_2(0, e^(2 i π x)) ϑ_2(0, e^(6 i π x)) + ϑ_3(0, e^(2 i π x)) ϑ_3(0, ... (2 terms)))

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