Properties

Name Z3, I3
Label 3.1.2.1.1
Class number 1
Dimension 3
Determinant 1
Level 2

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Lattice Invariants

Dimension:$3$
Determinant:$1$
Level:$2$
Label:$3.1.2.1.1$
Density:$0.523598775598298873077107230547\dots$
Group order:$48$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$1$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$, $(0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6q \) \(\mathstrut +\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut +\mathstrut 24q^{6} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 30q^{9} \) \(\mathstrut +\mathstrut 24q^{10} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut +\mathstrut 48q^{14} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 48q^{17} \) \(\mathstrut +\mathstrut 36q^{18} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 24q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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

This integral lattice is the Z3, I3 lattice.

This is the standard cubic lattice. This is the cubic P Bravais lattice of classical holotype..