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    Leech Lattice

    Description of lattice

    Description of lattice

    Lattice invariants

    dimension | 24
determinant | 1
minimal squared norm | 4
kissing number | 196560

    Lattice-packing invariants

    packing radius | 1
covering radius | sqrt(2)≈1.41421
density | π^12/479001600≈0.00192957
center density | 1
Hermite invariant | 4
thickness | (4 π^12)/467775≈7.90354
volume | 1

    Quadratic form and theta series

    quadratic form | 8 x_1^2 + 8 x_2 x_1 + 8 x_3 x_1 + 8 x_4 x_1 + 8 x_5 x_1 + 8 x_6 x_1 + 8 x_7 x_1 + 4 x_8 x_1 + 8 x_9 x_1 + 8 x_10 x_1 + 8 x_11 x_1 + ... + 2 x_14 x_24 + 2 x_15 x_24 + 2 x_16 x_24 - 2 x_17 x_24 + 2 x_18 x_24 + 2 x_19 x_24 + 2 x_20 x_24 + 4 x_21 x_24 + 4 x_22 x_24 + 4 x_23 x_24 (277 terms)
theta series (closed series) | 1/8 (ϑ_2(0, e^(i π x))^8 + ϑ_3(0, e^(i π x))^8 + ϑ_4(0, e^(i π x))^8)^3 - 45/16 ϑ_2(0, e^(i π x))^8 ϑ_3(0, e^(i π x))^8 ϑ_4(0, e^(i π x))^8

    More properties

    dual | Leech lattice
modular number | 1
number of symmetries | 8315553613086720000

    Common properties

    even | extremal | integral | unimodular

    Associated person

    John Leech

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