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Body-Centered Cubic Lattice

The body-centered cubic lattice, abbreviated BCC, is the cubic lattice consisting of points at the vertices and centers of the cubes in a simple cubic lattice. A realization is Z^3 union [Z^3+(1/2,1/2,1/2)]. Rescaling to covolume one gives

L_(BCC)=2^(-2/3){(m_1,m_2,m_3) in Z^3:m_1=m_2=m_3 (mod2)}.

For a Bravais lattice L of covolume one, define its renormalized Coulomb energy by

E(L)=lim_(kappa->0^+)(sum_(p in L\{0})(e^(-kappa||p||))/(||p||)-(4pi)/(kappa^2)).

Muratov and Novaga (2026) report a computer-assisted proof that L_(BCC) uniquely minimizes E(L), up to orthogonal transformations. Their comparison is among three-dimensional Bravais lattices of fixed covolume, not arbitrary point configurations or periodic crystals with multiple points per cell. The proof uses interval certificates which have not been independently rerun here. Muratov and Novaga (2026) report AI assistance with constructing, executing, and cross-checking the verification code.

See also

Bravais Lattice, Cubic Lattice, Point Lattice

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References

Muratov, C. B. and Novaga, M. "BCC Optimality for the Three-Dimensional Coulomb Lattice Energy." 21 Oct 2026. https://arxiv.org/abs/2610.29732.

Cite this as:

Weisstein, Eric W. "Body-Centered Cubic Lattice." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Body-CenteredCubicLattice.html

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