Get Math Help

GET TUTORING NEAR ME!

(800) 434-2582

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    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

    Back to List | POWERED BY THE WOLFRAM LANGUAGE