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Square Lattice

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Common name

2-dimensional cubic lattice

Description of lattice

basis | (1 | 0) | (0 | 1)
Gram matrix | (1 | 0
0 | 1)

Lattice invariants

dimension | 2
determinant | 1
minimal squared norm | 1
smallest vectors | (1 | 0) | (0 | 1) | (-1 | 0) | (0 | -1)
kissing number | 4

Lattice-packing invariants

packing radius | 1/2 = 0.5
covering radius | 1/sqrt(2)≈0.707107
density | π/4≈0.785398
center density | 1/4 = 0.25
Hermite invariant | 1
thickness | π/2≈1.5708
volume | 1

Quadratic form and theta series

quadratic form | x^2 + y^2
theta series (closed series) | ϑ_3(0, e^(i π x))^2

More properties

dual | integer lattice | 2
modular number | 1
number of symmetries | 8

Common properties

integral | odd | unimodular

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