Integral lattice 3.7.14.1.1

• Label: 3.7.14.1.1
• Class number: $1$
• Dimension: $3$
• Determinant: $7$
• Level: $14$

Lattice Invariants

Dimension:

$3$

Determinant:

$7$

Level:

$14$

Density:

$0.559750636120904659817410449045\dots$

Group order:

$12$

Hermite number:

$1.04551591714942043349659237432\dots$

Minimal vector length:

$2$

Kissing number:

$6$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 3 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 3 \end{array}\right)$
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Comments

This is the trigonal R Bravais lattice of classical holotype. Also called the rhombohedral R Bravais lattice..