lattice

Etymology

From Middle English latis, from Middle French lattis (“lathing”), from Old French lattis, from latte (“a lath”), from Frankish *latta (“a lath”), from Proto-Germanic *lattǭ, *lattō, *laþþō (“board; plank; ledge”), from Proto-Indo-European *(s)latn-, *(s)lat- (“beam; log”). Cognate with Old High German latta (“lath”), (German Latte), Old English lætt (“lath”), Middle Low German lāde (“plank, counter, sales counter”), German Laden (“shop”). More at lath.

noun

1. A flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.
   As we descended the long wooden stairway that leads from the central tower to the Island of Inchgarvie, the straight and simple outlines of the internal viaduct stood out in sharp contrast to the long sweep of the massive tubular arms of the cantilevers, and the complicated network of the lattice cross girders. 1950 March, H. A. Vallance, “On Foot Across the Forth Bridge”, in Railway Magazine, page 150
2. (heraldry) A bearing with vertical and horizontal bands that cross each other.
3. (crystallography) A regular spacing or arrangement of geometric points, often decorated with a motif.
4. (group theory) A discrete subgroup of Rⁿ which is isomorphic to Zⁿ (considered as an additive group) and spans the real vector space Rⁿ.
5. (music) A model of the tuning relationships of a just intonation system, comprising an array of points in a periodic multidimensional pattern.
6. (topology, Lie theory) A discrete subgroup L of a given locally compact group G whose quotient space G/L has finite invariant measure.
7. (algebra, order theory) A partially ordered set in which every pair of elements has a unique supremum and a unique infimum.

verb

1. To make a lattice of.
   to lattice timbers
2. To close, as an opening, with latticework; to furnish with a lattice.
   to lattice a window