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Properties

Name I1+A2
Label 3.3.6.1.2
Class number $1$
Dimension $3$
Determinant $3$
Level $6$

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Lattice Invariants

Dimension:$3$
Determinant:$3$
Level:$6$
Density:$0.302299894039036308432346376274\dots$
Group order:$24$
Hermite number:$0.693361274350634704843352274786\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 12 q^{3} \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 18 q^{6} \) \(\mathstrut +\mathstrut 12 q^{7} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 14 q^{9} \) \(\mathstrut +\mathstrut 12 q^{10} \) \(\mathstrut +\mathstrut 12 q^{11} \) \(\mathstrut +\mathstrut 12 q^{12} \) \(\mathstrut +\mathstrut 12 q^{14} \) \(\mathstrut +\mathstrut 36 q^{15} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 12 q^{17} \) \(\mathstrut +\mathstrut 42 q^{18} \) \(\mathstrut +\mathstrut 12 q^{19} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 2 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 2 \end{array}\right)$
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Comments

This integral lattice is the I1+A2 lattice.

This is the hexagonal P Bravais lattice of classical holotype..