View source for Lozenge (shape)

{{Short description|Quadrilateral with sides of equal length}}
{{redirect|◊||Diamond (disambiguation)}}
{{redirect|⟡|the extended play|Mujuk}}
{{Infobox symbol
|name=Lozenge
|mark=◊
|unicode = {{unichar|25CA|Lozenge|html=}}
|see also = {{unichar|2311|Square lozenge}}<br />{{unichar|29EB|Black lozenge}}<br />{{unichar|25C8|WHITE DIAMOND CONTAINING BLACK SMALL DIAMOND}}
}}

A '''lozenge''' ({{IPAc-en|ˈ|l|ɒ|z|ɪ|n|dʒ}}<ref>{{cite dictionary |url=https://www.macmillandictionary.com/dictionary/british/lozenge |title=lozenge |dictionary=[[Macmillan English Dictionary for Advanced Learners]]}}</ref> {{respell|LOZ|inj}}; symbol: {{char|◊}}), often referred to as a '''diamond''', is a form of [[rhombus]]. The definition of ''lozenge'' is not strictly fixed, and the word is sometimes used simply as a synonym ({{etymology|fro|{{wikt-lang|fro|losenge}}|}}) for ''rhombus''. Most often, though, lozenge refers to a thin rhombus—a rhombus with two acute and two obtuse angles, especially one with acute angles of 45°.<ref name="Mathworld">{{cite web|url=http://mathworld.wolfram.com/Lozenge.html |title=Lozenge - from Wolfram MathWorld |publisher=Mathworld.wolfram.com |date=2015-07-22 |access-date=2015-08-11}}</ref> The lozenge shape is often used in [[parquetry]] (with acute angles that are 360°/''n'' with ''n'' being an integer higher than 4, because they can be used to form a set of [[tile]]s of the same shape and size, reusable to cover the plane in various geometric patterns as the result of a tiling process called [[tessellation]] in mathematics) and as [[decorative art|decoration]] on [[ceramics (art)|ceramics]], [[Silver (household)|silverware]] and [[textile]]s. It also features in [[heraldry]] and [[Suit (cards)|playing cards]].

==Symbolism==
The lozenge motif dates from the [[Neolithic]] and [[Paleolithic art|Paleolithic]] period in [[Eastern Europe]] and represents a [[sown]] [[Field (agriculture)|field]] and female [[fertility]].<ref>{{cite book |first=Linda |last=Welters |title=Folk dress in Europe and Anatolia: beliefs about protection and fertility |publisher=[[Berg Publishers]] |year=1999 |pages=16–21 |isbn=1-85973-282-8 |url=https://books.google.com/books?id=35oIbNIIn-8C&q=lozenge+in+Ukrainian+embroidery&pg=PA16}}</ref> The ancient lozenge pattern often shows up in [[Diamond vault]] architecture, in traditional dress patterns of [[Slavic peoples]], and in traditional [[Ukrainian embroidery]]. The lozenge pattern also appears extensively in [[Celtic art]], art from the [[Ottoman Empire]], and ancient [[Phrygia]]n art.<ref>{{cite book |first=Gilbert |last=Sams |title=The early Phrygian pottery |publisher=Science Press |year=1994 |page=151 |isbn=0924171189 |url=https://books.google.com/books?id=KhBQCbBi-64C&q=lozenge&pg=PA151}}</ref>

The lozenge symbolism is one of the main symbols for women in [[Berber people|Berber]] carpets.<ref>Berber Carpets of Morocco: The Symbols Origin and Meaning, by [[Bruno Barbatti]], ACR Edition, {{ISBN|978-2-86770-184-9}}.</ref>
Common Berber jewelry from the [[Aurès Mountains]] or [[Kabylie]] in Algeria also uses this pattern as a female fertility sign.

In 1658, the English philosopher [[Sir Thomas Browne]] published ''[[The Garden of Cyrus]],'' subtitled ''The Quincunciall Lozenge, or Network Plantations of the Ancients,'' in which he outlined the [[mysticism|mystical]] interconnection of [[art]], [[nature]] and the [[universe]] via the [[quincunx]] pattern. He also suggested therein that ancient plantations were laid out in a lozenge pattern.<ref>{{cite book |first=Charles |last=Moore |title=The Poetics of Gardens |publisher=The MIT Press |year=1988 |page=161 |isbn=0262631539 |url=https://books.google.com/books?id=wnKiKy9_2u4C&q=quincuncial+lozenge&pg=PA161}}</ref>

Lozenges appear as [[symbol]]s in [[Classical element|ancient classic element systems]], in [[amulet]]s, and in [[religious symbolism]]. In [[playing card]]s, the symbol for the [[Suit (cards)|suit]] of ''diamonds'' is a lozenge.

==Applications==
{{more citations needed|section|date=November 2020}}

===Calculator===
[[File:Walther-Multa-32-Tastatur-rechte-Hälfte.jpg|thumb|upright|Lozenge (subtotal) key on a Walther Multa 32 calculator keyboard, {{circa|1970}}]]
On equipment, especially calculators, the lozenge is used to mark the subtotal key. It is standardized in ISO 7000<ref>ISO 7000 - Graphical symbols for use on equipment</ref> as symbol ISO-7000-0650 ("Subtotal"). In a similar fashion, the square lozenge (⌑), part of the [[BCDIC]] character set, was often used on tabulation listings to indicate second level totals in banking installations in the 1960s.<ref name="Mackenzie_1980">{{cite book |url=https://textfiles.meulie.net/bitsaved/Books/Mackenzie_CodedCharSets.pdf |title=Coded Character Sets, History and Development |series=The Systems Programming Series |author-last=Mackenzie |author-first=Charles E. |date=1980 |edition=1 |publisher=[[Addison-Wesley Publishing Company, Inc.]] |lccn=77-90165 |page=99 |isbn=978-0-201-14460-4 |access-date=2019-08-25 |archive-url=https://web.archive.org/web/20160526172151/https://textfiles.meulie.net/bitsaved/Books/Mackenzie_CodedCharSets.pdf |archive-date=May 26, 2016 |url-status=live |df=mdy-all }}</ref>

===Computing===
The [[APL (programming language)|APL programming language]] uses the lozenge, called ''diamond'', as [[Comparison of programming languages (syntax)#Statements|statement separator]].

===Camouflage===
[[File:Fokker D VII.jpg|thumb|left|A [[Fokker D.VII]] shows a four-color lozenge camouflage]]
{{Main|Lozenge camouflage}}
During the [[World War I|First World War]], the [[Germany|Germans]] developed [[lozenge camouflage]] (German: {{lang|de|Lozenge-Tarnung}}).<ref>{{cite web|url=http://www.wwiaviation.com/lozenge.html |title=German Lozenge {{notatypo|Camoflage}} |website=Wwiaviation.com |access-date=2015-08-11 |url-status=dead |archive-url=https://web.archive.org/web/20160306071242/http://www.wwiaviation.com/lozenge.html|archive-date=6 March 2016}}</ref> This camouflage was made up of colored [[polygon]]s of four or five colors. The repeating patterns often used irregular four-, five- and six-sided polygons, but some contained regular rhombi or hexagons. Because painting such a pattern was very time-consuming, and the paint added considerably to the weight of the aircraft, the pattern was printed on fabric. This pre-printed fabric was used from 1916 until the end of the war, in various forms and colours.

===Flags and emblems===
[[File:Flag of Brazil.svg|thumb|120px|[[Flag of Brazil]]]]
Several [[flag]]s feature lozenges, including the [[flag of Brazil]], which contains a yellow lozenge at the center. One official [[flag of Bavaria]] is entirely made of blue and white lozenges.

Several [[emblem]]s feature lozenges, including the [[Emblem of Uttarakhand]], one of the twenty-eight states of [[India]].

===Heraldry===
{{main|Lozenge (heraldry)}}
The lozenge in [[heraldry]] is a diamond-shaped [[charge (heraldry)|charge]], usually somewhat narrower than it is tall. A '''mascle''' is a voided lozenge—that is, a lozenge with a lozenge-shaped hole in the middle—and the rarer '''rustre''' is a lozenge containing a circular hole. A field covered in a pattern of lozenges is described as '''lozengy'''; a similar field of mascles is '''masculy'''.

===Mathematics===
In [[axiomatic set theory]], the lozenge refers to the principles known collectively as the [[diamond principle]].

===Medicine===
{{main|Throat lozenge}}
Cough tablets have taken the name lozenge, based on their original shape.  According to the ''[[Oxford English Dictionary]]'' the first use of this sense was in 1530.

In Finland, the lozenge is associated with [[salmiak]], through Apteekin Salmiakki. Thus, the lozenge is commonly called ''salmiakkikuvio'' "salmiak shape". The pattern is often used even if the candy is not actually lozenge-shaped.

===Military insignia===
====Finland====
In the [[Finnish military ranks|Finnish military]], the lozenge symbol is used in the [[insignia]] of conscripts undergoing officer training to signify their rank and progress. Conscript Officer Students, who are still in the early stages of their training, wear an insignia with one lozenge.<ref>{{Cite web |title=Military ranks |url=https://puolustusvoimat.fi/en/military-ranks |access-date=2024-08-28 |website=Puolustusvoimat |language=en-US}}</ref> As they advance in their training, they become Conscript Officer Candidates, identified by an insignia with two lozenges. This progression marks their nearing completion of officer training, with the lozenge serving as a clear visual indicator of their status.

====United States====
[[File:Ruptured Duck patch.JPG|thumb|upright|WWII "[[ruptured duck]]" Honorable Discharge Emblem lozenge]]
To implement 10 U.S.C 773, the Secretary of the Navy has prescribed the following distinctive mark for wear by members of military societies which are composed entirely of honorably discharged officers and enlisted personnel, or by the instructors and members of duly organized cadet corps.

"The distinctive mark will be a diamond, {{frac|3|1|2}} inches long by 2 inches wide, of any cloth material. A white distinctive mark will be worn on blue, green, or khaki clothing; and a blue distinctive mark will be worn on white clothing."{{citation needed|date=November 2020}}

"The distinctive mark will be worn on all outer clothing on the right sleeve, at the point of the shoulder, the upper tip of the diamond to be {{frac|1|4}} inch below the shoulder seam."{{citation needed|date=November 2020}}

The lozenge is used in the [[United States Army|Army]], [[United States Marine Corps|Marine Corps]], and [[United States Air Force|Air Force]] on the insignia of their respective [[first sergeant]]s. It is also used in the cadet programs of [[Army Reserve Officers' Training Corps|Army ROTC]], [[Junior Reserve Officers' Training Corps ranks|Army and Marine Corps Junior ROTC]], and the [[Civil Air Patrol]] as rank insignia of cadet officers corresponding to the military pay grades of O-4 to O-6 (Cadet Major, Cadet Lieutenant Colonel, and Cadet Colonel).{{Clear}}

===Visual arts===
[[File:Hals, Frans - Singing Girl - 1626-30.png|thumb|[[Girl Singing (Hals)|''Girl Singing'' by Frans Hals]], from about 1628, is an example of a painting in lozenge format.]]''Lozenge'' is the term used to identify the format of a two-dimensional work of art, typically a parallelogrammatic painting on a canvas, panel, or paper [[Support (art)|support]], that hangs as if from one of its corners. An example is ''Girl Singing'' by Frans Hals.<ref name="CHdG 1910">Hofstede de Groot, Cornelis (with the assistance of Kurt Freise and Dr Kurt Erasmus); ''A Catalogue Raisonné of the Works of the Most Eminent Dutch Painters of the Seventeenth Century, based on the work of John Smith, Volume III;'' translated from the German and edited by Edward G. Hawke; Macmillan & Co., London; 1910; pp. 32, 33. (On line at archive.org, retrieved 23 June 2024:  https://archive.org/details/catalogueraisonn03hofsuoft/page/32/mode/2up?view=theater)</ref>

===Modal logic===
In [[modal logic]], the lozenge expresses that there is "possibility". For example, the expression <math>\lozenge P</math> expresses that it is possible that <math>P</math> is true.

===Traffic signs===
[[File:Bicycle lane sign.svg|thumb|upright 0.5|[[Bicycle lane]]]]
The lozenge (technically a mascle) can be used on public roadways in the United States and Canada to mark a specific lane for a particular use. The lane will usually be painted with a lozenge at a regular interval, and signage will be installed to indicate the restrictions on using the lane. This marking is most often used to denote [[high-occupancy vehicle lane]]s or [[bus lane]]s, with accompanying signage reading "◊ HOV LANE" or "◊ BUS LANE" and giving the requirements for a vehicle to be accepted. Prior to 17 January 2006, lozenges could also be used to mark bicycle-only lanes, often in conjunction with a bicycle icon.<ref>{{cite web |url=https://mutcd.fhwa.dot.gov/htm/2009r1r2/intro/intro.htm#tableI02 |title=Introduction - MUTCD 2009 Edition - FHWA |publisher=[[United States Department of Transportation]] |access-date=2018-05-20}}</ref>

Starting in August 2023 on a four-years trial in France, a white lozenge on blue background reserves lanes to car-sharing vehicles (at least one passenger besides the driver).

In [[Japan]] and [[South Korea]], a lozenge marked in white paint on the road indicates an upcoming uncontrolled pedestrian crossing. Similarly, in [[New Zealand]] a lozenge marked in white paint on the road may be placed to indicate an upcoming pedestrian crossing. <ref>{{cite web |url=https://www.nzta.govt.nz/roadcode/general-road-code/about-other-road-users/sharing-the-road/sharing-the-road-with-pedestrians/#pedestrian_crossings |title=Sharing The Road With Pedestrians |publisher=[[NZ Transport Agency]] |access-date=2022-07-08}}</ref>

In the [[United Kingdom]], lozenges are used on tramway signs. For instance, speed limits are shown as a black lozenge on a white background, containing the speed limit in kilometres per hour.<ref>{{cite web |url=https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/519129/know-your-traffic-signs.pdf |title=Know Your Traffic Signs |publisher=[[Department for Transport]] |date=2007 |access-date=2018-05-20}}</ref>

[[File:Vienna Convention road sign B3-V1.svg|thumb|upright 0.5|[[Priority to the right|This road has priority]]]]
In many parts of Europe, [[Priority to the right|traffic from the right has right of way]] at all junctions, unless otherwise stipulated. A yellow lozenge is used (typically on major routes) to indicate that the rule does not apply to the current route.

A hollow lozenge is also used in the signage of waterways{{where|date=November 2020}} to identify a hazard. A cross is placed in the lozenge, dividing it in four, to mark a restricted area.<ref>{{cite web |url=http://www.marine-movers.com/AidsToNavigationExplained.html |title=Aids to Navigation Explained |website=marine-movers.com |archive-url=https://web.archive.org/web/20170727015122/http://www.marine-movers.com/AidsToNavigationExplained.html |archive-date=2017-07-27|url-status=dead}}</ref>{{Clear}}

==Square lozenge (Pillow symbol)<span class="anchor" id="Square lozenge"></span><span class="anchor" id="Travel industry"></span><span class="anchor" id="Pillow symbol"></span>==
A similar shape, {{char|{{big|'''⌑'''}}}}, with concavely curved edges instead of straight lines and oriented such that its edges lie up, down, left and right, is defined in the [[Miscellaneous Technical]] Unicode block as a '''square lozenge'''. It is used in [[travel agency|travel agencies]], where it appears on the specialist keyboards used with booking terminals, where it has the  familiar name, the '''pillow symbol'''.<ref>{{cite book |url=https://eportal.travelport.com/sites/GSWS/SiteCollectionDocuments/SGC/Portal/Documents/TrainingDocs/CourseBooks/CBPart1G360.pdf | title = Apollo for Travel Professionals |page = 1.4| date= 2007| access-date = 1 June 2020| publisher = Galileo International LLC)}}</ref>  In the 1960s, it was used in banking and for other purposes.<ref name="Mackenzie_1980"/>

==Encodings==
In [[Unicode]], the lozenge is encoded in multiple variants:
* {{unichar|22C4|DIAMOND OPERATOR|html=}}
* {{unichar|25CA|Lozenge|html=}}<ref>{{cite web|url=https://www.unicode.org/charts/PDF/U25A0.pdf |title=Geometric Shapes |publisher=Unicode.org |access-date=2015-08-11}}</ref>
* {{unichar|2662|WHITE DIAMOND SUIT|nlink=♢|html=}}{{efn|The term 'white' is perhaps a misnomer, since colour is font choice. A more accurate description might be 'outline'.}}
* {{unichar|2666|BLACK DIAMOND SUIT|nlink=♦|html=}}{{efn|The term 'black' is perhaps a misnomer, since colour is font choice. A more accurate description might be 'solid'.}}
* {{unichar|27E0|LOZENGE DIVIDED BY HORIZONTAL RULE|nlink=⟠|html=}}
* {{unichar|27E1|WHITE CONCAVE-SIDED DIAMOND}}
* {{unichar|29EB|BLACK LOZENGE|html=}}
* {{unichar|2B27|BLACK MEDIUM LOZENGE|html=}}
* {{unichar|2B28|WHITE MEDIUM LOZENGE|html=}}
* {{unichar|2B2A|BLACK SMALL LOZENGE|html=}}
* {{unichar|2B2B|WHITE SMALL LOZENGE|html=}}
* {{unichar|25C6|BLACK DIAMOND|html=}}
* {{unichar|25C7|WHITE DIAMOND|html=}}
* {{unichar|2756|Black Diamond Minus White X}}
* {{unichar|20DF|COMBINING ENCLOSING DIAMOND|html=|cwith=&emsp;}}
* {{unichar|1CC8D|INVERSE BLACK DIAMOND|html=}}<ref>{{cite web|url=https://www.unicode.org/charts/PDF/U1CC00.pdf |title=Symbols for Legacy Computing Supplement |publisher=Unicode.org |access-date=2024-12-22}}</ref>

The lozenge is present in [[DOS]] [[code page 437]] (at character code 4)<ref>{{cite book |first=Esko |last=Valtanen |title=DOS-OPAS |publisher=Teknolit |year=1990 |page=649 |isbn=952-90-1220-9}}</ref> and [[Mac-Roman]] (at character 215 = 0xd7). The [[AMS-LaTeX]] command for the lozenge is <code>\lozenge</code> (<math>\lozenge</math>).

Other related unicode characters include:
* {{unichar|2311|SQUARE LOZENGE|html=}}
* {{unichar|2726|BLACK FOUR POINTED STAR|html=}}
* {{unichar|2727|WHITE FOUR POINTED STAR|html=}}

In IBM 026 [[punched card]] code the pillow-shaped square "lozenge" {{large|⌑}} is (12-8-4).<ref>{{cite web |url=http://www.columbia.edu/cu/computinghistory/026.html |title=The IBM 026 Key Punch |publisher=[[Columbia University]] |date=2003-12-31 |access-date=2018-05-20}}</ref><ref name="Mackenzie_1980"/>

{{Clear}}

==Imagery==
<gallery>
File:Rhombus.png|Lozenge
File:Museum of Anatolian Civilizations068.jpg|Phrygian art, 7th Century BC
File:MotherGoddessFertility.JPG|[[Cucuteni–Trypillia culture|Cucuteni-Trypillian]] figurine with sown field pattern
File:Lozenge.jpg|[[Bush Barrow]] Lozenge [[British Bronze Age]]
File:Antique oushak carpet with a pale red and green tone.jpg|[[Ushak carpet]], [[Ottoman Empire]]
File:Yantprapidta.JPG|[[Khatha]], sacred [[Yantra]] amulet from [[Thailand]]
File:Ashthalakshmi - Star of Laxmi.svg|[[Hindu]] [[Star of Lakshmi]]
File:ROUB EL HIZB 06DE.svg|[[Muslim]] [[Rub el Hizb]]
File:Magic square at the Parshvanatha temple, Khajuraho.png|[[Magic squares]] were used as [[amulets]]
File:Talis02.png|[[Talisman]] design from an 18th-century French [[grimoire]]
File:Qur'an 4475.jpg|[[Arabic]] manuscript [[China]], 16th Century
File:Carolus Magnus denarus Tarvisii.jpg|[[Charlemagne]] coins, [[French denier|denier]] or denaro {{circa|771}}–793
File:Dish with floral lozenge from the Belitung shipwreck, ArtScience Museum, Singapore - 20110618.jpg|[[Belitung shipwreck]], [[Tang dynasty]] {{circa|825}}
File:Berezhany- (267).jpg|Traditional sown field pattern of [[Western Ukraine]]
File:Armenian rug-9 Kazak.jpg|[[Armenia]]n tapestry
File:RR 02.png|[[Rongorongo]] [[proto-writing]], possible [[lunar calendar]] calculating device
File:Epigonation (1911).jpg|[[Epigonation]] in [[Eastern Christianity]]
File:Four elements representation.svg|[[Greece|Greek]] [[Classical element]]s
File:COAabbess.png|In [[Ecclesiastical heraldry]] [[Lozenge (heraldry)|lozenge shape]] is reserved for women
File:WASPbadge.jpg|[[Women Airforce Service Pilots Badge]]
File:Roundel of the Philippines.svg|[[Philippine Air Force]] roundel
File:Mitsubishi motors new logo.svg|[[Mitsubishi]] logo
File:Renault 2021.svg|[[Renault]] logo
File:SV-Werder-Bremen-Logo.svg|[[SV Werder Bremen]] crest
File:Flag of Belarus.svg|National flag of [[Belarus]] with sown field pattern
File:Flag of Saint Vincent and the Grenadines.svg|National flag of [[Saint Vincent and the Grenadines]]
File:Arms of Catherine Middleton.svg|[[Lozenge (heraldry)|Lozenge-shaped]] coat of arms is reserved for women
File:White d a.svg|[[Ace of diamonds]]
File:Peterpaul sfbgewoelbe.JPG|[[Diamond vault]] in German architecture
File:Ledringhem-runes.jpg|''Rune''-shaped designs (five-lozenges cross and heart) on the gable of [[Ledringhem]]'s church
File:Moforlogiaagrária.jpg|Sown fields in an [[open field system]] of farming
</gallery>

==See also==
* [[Parallelepiped]], 3-D Lozenge
* [[Petrosomatoglyph]], lozenges as symbols in prehistory

==Notes==
{{notelist}}

==References==
{{Reflist}}

==External links==
* {{Wiktionary-inline|lozenge}}

{{navbox punctuation}}

[[Category:Types of quadrilaterals]]
[[Category:Logic symbols]]