Even unimodular lattice

An integral quadratic lattice that is both an even lattice and a unimodular lattice. The K3 intersection lattice has signature $(3,19)$, while the positive-definite E8 lattice has rank eight.

The positive-definite rank-eight even unimodular lattice can be realized as vectors in ${\mathbb{Z}}^8$ or $(\mathbb{Z}+1/2{)}^8$ whose coordinate sum is even, with the ordinary Euclidean inner product. Negating this form gives $E_8(-1)$ in the K3 intersection lattice.