Quincunx

A quincunx of pips on the fifth side of a die

A quincunx /ˈkwɪn.kʌŋks/ is a geometric pattern consisting of five points arranged in a cross, with four of them forming a square or rectangle and a fifth at its center.^[1] It forms the arrangement of five units in the pattern corresponding to the five-spot on six-sided dice, playing cards, or dominoes. It is represented in Unicode as U+2059 ⁙ five dot punctuation or (for the dice pattern) U+2684 ⚄ die face-5.

Historical origins of the name

A quincunx coin

Portuguese shield

The quincunx was originally a coin issued by the Roman Republic c. 211–200 BC, whose value was five twelfths (quinque + uncia) of an as, the Roman standard bronze coin. On the Roman quincunx coins, the value was sometimes indicated by a pattern of five dots or pellets. However, these dots were not always arranged in a quincunx pattern.

Examples

Quincunx patterns occur in many contexts:

The flag of the Solomon Islands features a quincunx of stars.

A quincuncial map

Cosmatesque pavements with the quincunx pattern

• In heraldry, groups of five elements (charges) are often arranged in a quincunx pattern, called in saltire in heraldic terminology. The flag of the Solomon Islands features this pattern, with its five stars representing the five main island groups in the Solomon Islands. Another instance of this pattern occurs in the flag of the Republic of Yucatán, where it symbolized the five departments into which the republic was divided.
• A quincunx is a standard pattern for planting an orchard.^[2]
• Quincunxes are used in modern computer graphics as a pattern for multisample anti-aliasing. Quincunx antialiasing samples scenes at the corners and centers of each pixel. These five sample points, in the shape of a quincunx, are combined to produce each displayed pixel. However, samples at the corner points are shared with adjacent pixels, so the number of samples needed is only twice the number of displayed pixels.^[3]
• In numerical analysis, the quincunx pattern describes the two-dimensional five-point stencil, a sampling pattern used to derive finite difference approximations to derivatives.^[4]
• In architecture, a quincuncial plan, also defined as a "cross-in-square", is the plan of an edifice composed of nine bays. The central and the four angular ones are covered with domes or groin vaults so that the pattern of these domes forms a quincunx; the other four bays are surmounted by barrel vaults.^[5] In Khmer architecture, the towers of a temple, such as Angkor Wat, are sometimes arranged in a quincunx to represent the five peaks of Mount Meru.^[6]
• A quincunx is one of the quintessential designs of Cosmatesque inlay stonework.^[7]
• A quincuncial map is a conformal map projection that maps the poles of the sphere to the centre and four corners of a square, thus forming a quincunx.
• The points on each face of a unit cell of a face-centred cubic lattice form a quincunx.
• The quincunx as a tattoo is known as the five dots tattoo. It has been variously interpreted as a fertility symbol,^[8] a reminder of sayings on how to treat women or police,^[9] a recognition symbol among the Romani people,^[9] a group of close friends,^[10] standing alone in the world,^[11] or time spent in prison (with the outer four dots representing the prison walls and the inner dot representing the prisoner).^[12] Thomas Edison, whose many inventions included a tattooing machine, had this pattern tattooed on his forearm.^[13]
• Republican Roman manipular legions adopted a checkered formation called quincunx when deployed for battle.
• The first two stages of the Saturn V moon rocket had engines in a quincunx arrangement.^[14]

Literary symbolism

Various literary works use or refer to the quincunx pattern for its symbolic value:

• The English physician Sir Thomas Browne in his philosophical discourse The Garden of Cyrus (1658) elaborates upon evidence of the quincunx pattern in art, nature and mystically as evidence of "the wisdom of God". Although Browne wrote about quincunx in its geometric meaning, he may also have been influenced by English astrology, as the astrological meaning of "quincunx" (unrelated to the pattern) had recently come into vogue.^[15]
• James Joyce uses the term in Grace, a short story in The Dubliners of 1914, to describe the seating arrangement of five men in a church service. Lobner^[16] argues that in this context the pattern serves as a symbol both of the wounds of Christ and of the Greek cross.
• Lawrence Durrell's novel-sequence The Avignon Quintet is arranged in the form of a quincunx, according to the author; the final novel in the sequence is called Quinx, the plot of which includes the discovery of a quincunx of stones.^[17]
• The Quincunx (ISBN 0-345-37113-5) is the title of a lengthy and elaborate novel by Charles Palliser set in 19th-century England, published in 1989; the pattern appears in the text as a heraldic device, and is also reflected in the structure of the book.^[18]
• In the first chapter of The Rings of Saturn, W.G. Sebald's narrator cites Browne's writing on the quincunx. The quincunx in turn becomes a model for the way in which the rest of the novel unfolds.^[19]
• Séamus Heaney describes Ireland's historical provinces as together forming a quincunx, as the Irish word for province cúige (literally: "fifth part") also explicates. The five provinces of Ireland were Ulster (north), Leinster (east), Connacht (west), Munster (south) and Meath (center, and now a county within Leinster). More specifically, in his essay Frontiers of Writing, Heaney creates an image of five towers forming a quincunx pattern within Ireland, one tower for each of the five provinces, each having literary significance.^[20][21]

References

Wikimedia Commons has media related to Quincunxes.