TOPICS
Search

Unit Lattice

A point lattice which can be constructed from an arbitrary parallelogram of unit area. For any such planar lattice, the minimum distance c between any two points is a quantity characteristic of the lattice. This distance satisfies

c<=sqrt(2/(sqrt(3)))

(Hilbert and Cohn-Vossen 1999, p. 36). For a lattice in three dimensions,

c<=2^(1/6)

(Hilbert and Cohn-Vossen 1999, p. 45).

See also

Hypersphere Packing, Point Lattice, Sphere Packing

Explore with Wolfram|Alpha

References

Hilbert, D. and Cohn-Vossen, S. Geometry and the Imagination. New York: Chelsea, 1999.

Referenced on Wolfram|Alpha

Unit Lattice

Cite this as:

Weisstein, Eric W. "Unit Lattice." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UnitLattice.html

Subject classifications