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lattice - Wiktionary, the free dictionary

From Wiktionary, the free dictionary

A wooden lattice
A lattice (order theory)

From Middle English latis, from Middle French lattis (“lathing”), from Old French lattis, from latte (“a lath”), from Frankish *lattā, *lattu (“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.

lattice (plural lattices)

  1. A flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.

    • 1826, [Mary Shelley], chapter VII, in The Last Man. […], volume II, London: Henry Colburn, […], →OCLC:

      It was now in ruin: the deer had climbed the broken palings, and reposed among the flowers; grass grew on the threshold, and the swinging lattice creaking to the wind, gave signal of utter desertion.

    • 1950 March, H. A. Vallance, “On Foot Across the Forth Bridge”, in Railway Magazine, page 150:

      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.

  2. (heraldry) A bearing with vertical and horizontal bands that cross each other.
    Coordinate terms: fret, trellis
  3. (crystallography) A regular spacing or arrangement of geometric points, often decorated with a motif.
  4. (music) A model of the tuning relationships of a just intonation system, comprising an array of points in a periodic multidimensional pattern.
  5. (mathematics, algebra) In any of several technical senses, a substructure with properties analogous to those the set of points with integer coordinates bears in relation to the full Euclidian space these points are contained in.
    2. (group theory) A discrete subgroup of Rn which is isomorphic to Zn (considered as an additive group) and which spans the real vector space Rn.
    3. (topology, Lie theory, generalizing sense 5.1) A discrete subgroup L of a given locally compact group G whose quotient space G/L has finite invariant measure.
    4. (algebra, ring theory, generalizing sense 5.1, with respect to a vector space V over a field F which is the field of fractions of an integral domain R in F) A finitely generated R-submodule of V which spans V over F. (In this case the submodule is called an R-lattice).
  6. (mathematics, order theory) A partially ordered set in which every pair of elements has a unique supremum and a unique infimum.
  • (flat panel constructed with strips of wood or other material): latticework

flat panel constructed with strips of wood or other material

regular spacing or arrangement of geometric points

partially ordered set

Translations to be checked

lattice (third-person singular simple present lattices, present participle latticing, simple past and past participle latticed)

  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

Variant of latice influenced by latte (“milk”).

lattice m (plural lattici)

  1. latex