The $A_2$ lattice, also known as the hexagonal lattice, is the root lattice associated to the $A_2$ and $G_2$ root systems.
Lattice Invariants
Dimension: | $2$ |
Determinant: | $3$ |
Level: | $3$ |
Density: | $0.906899682117108925297039128820\dots$ |
Group order: | $12$ |
Hermite number: | $1.15470053837925152901829756100\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $6$ |
Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rr} 2 & -1 \\ -1 & 2 \end{array}\right)$
Genus Structure
Class number: | $1$ |
$\left(\begin{array}{rr} 2 & 1 \\ 1 & 2 \end{array}\right)$ | |
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Comments
This integral lattice is the A2 lattice.
This is a root lattice.
Additional information
This lattice is the unique solution of the sphere packing problem and the general kissing number problem in dimension 2.