Lozenge

A lozenge () is a form of rhombus. The definition of lozenge is not strictly fixed, and it is sometimes used simply as a synonym (from the French losange) for rhombus. Most often, though, lozenge refers to a thin rhombus — a rhombus with acute angles of 45°.[1] The lozenge shape is often used in parquetry and as decoration on ceramics, silverware, and textiles.

Applications

Modal logic

In modal logic, the lozenge expresses the possibility of the following expression. For example, the expression ${\displaystyle \Diamond P}$ expresses that it is possible that P is true.

Mathematics

In axiomatic set theory, the lozenge refers to the principles known collectively as diamondsuit.

Camouflage

During the First World War, the Germans were looking for a way to effectively camouflage their aircraft. This resulted in the development of the so-called lozenge pattern (Lozengetarnung), made up of irregularly shaped colored polygons (not necessarily actual rhombi). Because painting such a pattern was very time consuming, and the paint added considerably to the weight of the aircraft, it was decided to print the pattern on fabric. This pre-printed fabric was used from 1916 onwards, in various forms and colours. The most notable of these were the day fighter used variations-the five color version, usually nicknamed "Canberra" from its existence on the Australian War Memorial's Albatros D.Va aircraft, and the four color version, nicknamed "Knowlton" from its existence on the Brome County Historical Society's Fokker D.VII aircraft in the Knowlton suburb of Lac-Brome, Quebec, Canada. Both the Canberra and Knowlton patterns had sets of darker shades of their colors for upper surface application, and lighter shades for underside application.

Heraldry

The lozenge in heraldry is a diamond-shaped 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.

Cough tablets

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.

The glyph

The lozenge glyph is found in DOS code page 437 (at character code 4)[2] and Mac-Roman. It is also found at Unicode 0x25CA. In HTML it can be typed with &loz; (or &#9674; or &#x25CA;), which will produce ◊ (and ◊ and ◊).

U.S. Military

The lozenge is used in the U.S. Army, Marine Corps, and Air Force on the insigniae of their respective First Sergeants.

Transportation

The lozenge can be used on public roadways in the United States 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 lanes, with accompanying signage reading "◊ HOV LANE" and giving the requirements for a vehicle to be accepted as "high-occupancy". Lozenges can also be used to mark bicycle-only lanes, often in conjunction with a bicycle icon.