lattice

English

A wooden lattice

A lattice (order theory)

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.

Pronunciation

• (UK, US) IPA^(key): /ˈlæt.ɪs/

• Audio (UK)

  (file)

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, The Last Man, part 2, chapter 7,

     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.

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.

Synonyms

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

Hyponyms

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

Hypernyms

• (order theory) partially ordered set

Derived terms

Derived terms

• Boolean lattice
• complete lattice
• crystal lattice
• distributive lattice
• lattice bridge

• lattice energy
• lattice girder
• {{l|en|lattice model}
• lattice plant
• lattice point

• lattice window
• semilattice
• skew lattice
• space lattice

Translations

flat panel constructed with strips of wood or other material

• Czech: mřížka f
• Dutch: raster (nl) n
• Finnish: säleikkö (fi), ristikko (fi)
• French: treillis (fr)
• Galician: latiza f
• German: Gitterzaun m, Gitterwerk n, Gitter (de) n, Gatter (de) n, Lattengerüst (de) n
• Greek: καφάσι (el) n (kafási)

• Italian: grata (it) f, graticcio (it) m, cannicciata f
• Japanese: 格子 (kōshi)
• Portuguese: gelosia (pt) f, rótula (pt) f, treliça (pt) f
• Russian: плетёная (ru) (pletjónaja) решётка (ru) f (rešótka)
• Scottish Gaelic: cliath f
• Spanish: celosía (es) f
• Tagalog: sala-sala

regular spacing or arrangement of geometric points

• Chinese:

  Mandarin: 晶格 (zh) (jīnggé)

• Dutch: rooster (nl), kristalrooster
• Finnish: hila (fi)
• French: quadrillage (fr), grille (fr), lattis (fr)
• German: Kristallgitter (de) n, Gitter (de) n
• 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)
• Portuguese: trama (pt) f, grade (pt) f
• Romanian: rețea (ro), latice
• Russian: решётка (ru) f (rešótka)
• Spanish: trama (es), cuadrícula (es)

partially ordered set

• Chinese:

  Mandarin: 格 (zh) (gé)

• Czech: svaz (cs) m
• Dutch: tralie (nl)
• Estonian: võre
• German: Verband (de) m
• Hungarian: háló (hu)
• Icelandic: grind (is) f

• Italian: reticolo (it) m
• Japanese: 束 (ja) (そく, soku)
• Macedonian: решетка f (réšetka)
• 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, removing any numbers. Numbers do not necessarily match those in definitions. 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
• Hebrew: ^{(please verify)} סבכה‎‎ (he) f (svaha), ^{(please verify)} רשת‎‎ f (rešet)
• 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)
• Spanish: ^{(please verify)} celosía (es) f, ^{(please verify)} rejilla (es) f, (1) ^{(please verify)} enrejado (es) m, ^{(please verify)} reticulado m, ^{(please verify)} latis m, (2) ^{(please verify)} enrejado (es) m
• 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, G. & C. Merriam, 1913
• lattice in The Century Dictionary, The Century Co., New York, 1911

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
• Lattices on Wikimedia Commons.Wikimedia Commons

Anagrams

• tactile, talcite

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Italian

Noun

lattice m (plural lattici)

1. latex

Synonyms

• latex

Anagrams

• caletti