1. [n]  framework consisting of an ornamental design made of strips of wood or metal
2. [n]  small opening (like a window in a door) through which business can be transacted
3. [n]  an arrangement of points or particles or objects in a regular periodic pattern in 2 or 3 dimensions

1. \Lat"tice\, n. [OE. latis, F. lattis lathwork, fr. latte
   lath. See {Latten}, 1st {Lath}.]
   1. Any work of wood or metal, made by crossing laths, or thin
      strips, and forming a network; as, the lattice of a
      window; -- called also {latticework}.
            The mother of Sisera looked out at a window, and
            cried through the lattice.            --Judg. v. 28.
   2. (Her.) The representation of a piece of latticework used
      as a bearing, the bands being vertical and horizontal.
   {Lattice bridge}, a bridge supported by lattice girders, or
      latticework trusses.
   {Lattice girder} (Arch.), a girder of which the wed consists
      of diagonal pieces crossing each other in the manner of
      latticework.
   {Lattice plant} (Bot.), an aquatic plant of Madagascar
      ({Ouvirandra fenestralis}), whose leaves have interstices
      between their ribs and cross veins, so as to resemble
      latticework. A second species is {O. Berneriana}. The
      genus is merged in {Aponogeton} by recent authors.
   

2. \Lat"tice\, v. i. [imp. & p. p. {Latticed}; p. pr. & vb.
   n. {Latticing}.]
   1. To make a lattice of; as, to lattice timbers.
   2. To close, as an opening, with latticework; to furnish with
      a lattice; as, to lattice a window.
   {To lattice up}, to cover or inclose with a lattice.
            Therein it seemeth he [Alexander] hath latticed up
            C[ae]sar.                             --Sir T.
                                                  North.
   

A partially ordered set in which all finite subsets have a least upper bound and greatest lower bound.

This definition has been standard at least since the 1930s and probably since Dedekind worked on lattice theory in the 19th century; though he may not have used that name.

See also complete lattice, domain theory.

(1.) Heb. 'eshnabh, a latticed opening through which the cool breeze passes (Judg. 5:28). The flat roofs of the houses were sometimes enclosed with a parapet of lattice-work on wooden frames, to screen the women of the house from the gaze of the neighbourhood.

(2.) Heb. harakim, the network or lattice of a window (Cant. 2:9).

(3.) Heb. sebakhah, the latticed balustrade before a window or balcony (2 Kings 1:2). The lattice window is frequently used in Eastern countries.