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    Coxeter-Todd Lattice

    Common names

    K12 | Coxeter-Todd lattice

    Lattice invariants

    dimension | 12 determinant | 729 minimal squared norm | 4 kissing number | 756

    Lattice-packing invariants

    packing radius | 1 covering radius | 2 sqrt(2/3)≈1.63299 density | π^6/19440≈0.0494542 center density | 1/27≈0.037037 Hermite invariant | 4/sqrt(3)≈2.3094 thickness | (16384 π^6)/885735≈17.7834 volume | 27

    Quadratic form and theta series

    theta series (closed series) | 9/32 ϑ_2(0, e^(i π x))^6 ϑ_2(0, e^(3 i π x))^6 + 45/16 ϑ_2(0, e^(i π x))^4 (ϑ_2(0, e^(4 i π x)) <<1>>(<<1>>) + ... (2 terms))^2 ϑ_2(0, e^(3 i π x))^4 + (ϑ_2(0, e^(4 i π x)) ϑ_2(0, e^(12 i π x)) + ϑ_3(0, e^(4 i π x)) ϑ_3(0, e^(12 i π x)))^6

    More properties

    modular number | 3 number of symmetries | 78382080

    Common properties

    extremal | integral | nonunimodular

    Associated people

    Harold Scott MacDonald Coxeter | John Arthur Todd

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