Integral lattice 3.128.8.1.1 (A3*, D3*)

• Name: A3*, D3*
• Label: 3.128.8.1.1
• Class number: $1$
• Dimension: $3$
• Determinant: $128$
• Level: $8$

The $A_3^*$ lattice, also known as the body-centered cubic lattice, is the dual of the $A_3$ lattice.

Lattice Invariants

Dimension:

$3$

Determinant:

$128$

Level:

$8$

Density:

$0.680174761587831693972779346617\dots$

Group order:

$48$

Hermite number:

$1.19055078897614960606377922945\dots$

Minimal vector length:

$6$

Kissing number:

$8$

Normalized minimal vectors:

$(1, 0, 0)$, $(1, 1, 1)$, $(0, 1, 0)$, $(0, 0, 1)$

Download this list for gp, magma, sage

Theta Series

Gram Matrix

$\left(\begin{array}{rrr} 6 & -2 & -2 \\ -2 & 6 & -2 \\ -2 & -2 & 6 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrr} 6 & -2 & -2 \\ -2 & 6 & -2 \\ -2 & -2 & 6 \end{array}\right)$
	Download this matrix for gp, magma, sage

Comments

This integral lattice is the A3*, D3* lattice.

This is the cubic I Bravais lattice of even holotype. This is the body centered cubic lattice.

Additional information

This is the cubic I Bravais lattice of even holotype.