Integral lattice 3.10.20.1.1

• Label: 3.10.20.1.1
• Class number: $1$
• Dimension: $3$
• Determinant: $10$
• Level: $20$

Lattice Invariants

Dimension:

$3$

Determinant:

$10$

Level:

$20$

Density:

$0.468320982069381759543758309547\dots$

Group order:

$12$

Hermite number:

$0.928317766722555778482015270183\dots$

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

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 4 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 4 \end{array}\right)$
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Comments

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