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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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