lattice

English

A wooden lattice

A lattice (order theory)

Alternative forms

• lettice (archaic)

Etymology

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.

Pronunciation

• (UK, US) IPA^(key): /ˈlæt.ɪs/

• Audio (UK):

  (file)

• Rhymes: -ætɪs

Noun

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.

Synonyms

• (flat panel constructed with strips of wood or other material): latticework

Hypernyms

• (order theory) partially ordered set

Hyponyms

• (group theory): cubic lattice, integer lattice, square lattice (n=2)
• (order theory) complete lattice, distributive lattice

Derived terms

• Abrikosov lattice
• antilattice
• Bethe lattice
• bilattice
• Boolean lattice
• bounded lattice
• Bravais lattice
• complete lattice
• crystal lattice
• distributive lattice
• hyperlattice
• interlattice
• lattice Boltzmann method
• lattice bridge
• lattice constant
• lattice energy
• lattice girder
• lattice leaf
• latticelike
• lattice model
• lattice parameter
• lattice plant
• lattice point
• lattice theory
• lattice window
• latticewise
• lattice-work
• Leech lattice
• microlattice
• nanolattice
• Niemeier lattice
• nonlattice
• optical lattice
• quasilattice
• reciprocal lattice
• semilattice
• skew lattice
• space lattice
• spin-lattice relaxation time
• sublattice
• superlattice
• Tamari lattice

Descendants

• → Japanese: ラティス (ratisu)

Translations

flat panel constructed with strips of wood or other material

• Bulgarian: решетка (bg) f (rešetka)
• Catalan: gelosia (ca) f
• Czech: mřížka (cs) f
• Dutch: raster (nl) n, latwerk (nl) n
• Finnish: säleikkö (fi), ristikko (fi)
• French: treillis (fr)
• Galician: latiza f, encanivelado m, xeloxía f
• German: Gitterzaun m, Gitterwerk (de) n, Gitter (de) n, Gatter (de) n, Lattengerüst (de) n
• Greek: καφασωτό (el) n (kafasotó), καφάσι (el) n (kafási)
• Hebrew: סריג m (saríg), סבכה (he) f (svakhá)
• Hungarian: rács (hu), rácsozat (hu), apácarács, ablakrács (hu), lécezet (hu), rostély (hu)
• Italian: grata (it) f, graticcio (it) m, cannicciata f
• Japanese: 格子 (ja) (kōshi), ラティス (ratisu)
• Ladino: bagdadi
• Latin: cancellī m pl, clāthrī m pl
• Macedonian: решетка f (rešetka)
• Polish: krata (pl) f, kratka (pl) f
• Portuguese: gelosia (pt) f, rótula (pt) f, treliça (pt) f
• Russian: плетёная решётка f (pletjónaja rešótka)
• Scottish Gaelic: cliath f
• Spanish: celosía (es) f, enrejado (es) m, entramado (es) m
• Tagalog: sala-sala

regular spacing or arrangement of geometric points

• Bulgarian: решетка (bg) f (rešetka)
• Catalan: quadrícula f
• Chinese:

  Mandarin: 晶格 (zh) (jīnggé)

• Dutch: rooster (nl), kristalrooster (nl)
• Finnish: hila (fi)
• French: quadrillage (fr), grille (fr), lattis (fr), réseau (fr) m
• German: Kristallgitter (de) n, Gitter (de) n
• Greek: πλέγμα (el) n (plégma)
• Hebrew: רשת (he) f (réshet)
• Hungarian: rács (hu)
• Italian: graticcio (it) m, traliccio (it) m, reticolo (it) m, griglia (it) f
• Japanese: 結晶格子 (kesshōkōshi)
• Korean: 결정격자 (gyeoljeonggyeokja)
• Macedonian: ре́шетка f (réšetka)
• Polish: krata (pl) f
• Portuguese: trama (pt) f, grade (pt) f
• Romanian: rețea (ro), latice
• Russian: решётка (ru) f (rešótka)
• Spanish: trama (es), cuadrícula (es), red cristalina f, retícula (es) f

partially ordered set

• Chinese:

  Mandarin: 格 (zh) (gé)

• Czech: svaz (cs) m
• Dutch: tralie (nl)
• Estonian: võre
• Finnish: hila (fi)
• German: Verband (de) m
• Greek: πλέγμα (el) n (plégma)
• Hebrew: סריג m (saríg)
• Hungarian: háló
• Icelandic: grind (is) f
• Italian: reticolo (it) m
• Japanese: 束 (ja) (そく, soku), ラティス (ratisu)
• Macedonian: решетка f (rešetka)
• Polish: krata (pl) f
• Portuguese: reticulado m
• Russian: решётка (ru) f (rešótka)
• Spanish: retículo (es) m

The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.

Translations to be checked

• French: ^{(please verify)} treillage (fr) m, ^{(please verify)} treillis (fr) m, ^{(please verify)} grillage (fr) m
• Hindi: ^{(please verify)} झिलमिली (hi) (jhilmilī), ^{(please verify)} जालक (hi) (jālak), ^{(please verify)} झंझरी (jhañjhrī), ^{(please verify)} लकड़ी या लोहे की जाली (lakṛī yā lohe kī jālī)
• Korean: ^{(please verify)} 격자 (gyeokja), ^{(please verify)} 격자창 (gyeokjachang)
• Latin: ^{(please verify)} cancelli m pl
• Mandarin: ^{(please verify)} 梯 (zh) (tī)
• Swedish: ^{(please verify)} gitter (sv) c

See also

• grid

Verb

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

References

• “lattice”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• William Dwight Whitney, Benjamin E[li] Smith, editors (1911), “lattice”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC.

Further reading

• Latticework on Wikipedia.Wikipedia
• Lattice (order) on Wikipedia.Wikipedia
• Lattice (group) on Wikipedia.Wikipedia
• Lattice (discrete subgroup) on Wikipedia.Wikipedia
• Lattice (music) on Wikipedia.Wikipedia
• Primitive cell on Wikipedia.Wikipedia
• Category:Lattices on Wikimedia Commons.Wikimedia Commons

Anagrams

• tactile, talcite

Italian

Etymology

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

Pronunciation

• IPA^(key): /ˈlat.ti.t͡ʃe/
• Rhymes: -attitʃe
• Hyphenation: làt‧ti‧ce

Noun

lattice m (plural lattici)

1. latex

Further reading

• lattice on the Italian Wikipedia.Wikipedia ^it

Anagrams

• caletti