Integral lattice 3.1.2.1.1 (Z3, I3)

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

Lattice Invariants

Dimension:

$3$

Determinant:

$1$

Level:

$2$

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

Gram Matrix

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

Genus Structure

Genus representatives:

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