different between lattice vs holohedry

English

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 *latt?, *latt?, *laþþ? (“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 l?de (“plank, counter, sales counter”), German Laden (“shop”). More at lath.

Pronunciation

• (UK, US) IPA^(key): /?læt.?s/

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.
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

Translations

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.

2. To close, as an opening, with latticework; to furnish with a lattice.

References

• lattice in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• lattice in The Century Dictionary, New York, N.Y.: The Century Co., 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

Italian

Etymology

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

Pronunciation

• IPA^(key): /?lat.ti.t??e/
• Rhymes: -attit?e

Noun

lattice m (plural lattici)

1. Alternative form of latice (“latex”)

   Synonym: latex

Further reading

• lattice on the Italian Wikipedia.Wikipedia ^it

Anagrams

• caletti

English

Noun

holohedry (countable and uncountable, plural holohedries)

1. The condition of a crystal whose point group is identical to that of its lattice.

Related terms

• holohedral

Translations