geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, a hendecagram (also endecagram or endekagram) is a

star polygon In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, Decagram (geometry)#Related figures, certain notable ones can ...

that has eleven vertices. The name ''hendecagram'' combines a Greek

numeral prefix Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: *triangle, quadrilateral, pentagon, hexagon, octagon ...

, '' hendeca-'', with the

Greek Greek may refer to: Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group *Greek language, a branch of the Indo-European language family **Proto-Greek language, the assumed last common ancestor of all kno ...

suffix '' -gram''. The ''hendeca-'' prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning "

eleven Eleven or 11 may refer to: *11 (number) * One of the years 11 BC, AD 11, 1911, 2011 Literature * ''Eleven'' (novel), a 2006 novel by British author David Llewellyn *''Eleven'', a 1970 collection of short stories by Patricia Highsmith *''Eleven'' ...

". The ''-gram'' suffix derives from γραμμῆς (''grammēs'') meaning a line.

Regular hendecagrams

There are four regular hendecagrams, which can be described by the notation , , , and ; in this notation, the number after the slash indicates the number of steps between pairs of points that are connected by edges. These same four forms can also be considered as stellations of a regular

hendecagon In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name ''hendecagon'', from Greek ''hendeka'' "eleven" and ''–gon'' "corner", is often preferred to the hybrid ''undecagon'', whose first part is f ...

. Since 11 is prime, all hendecagrams are star polygons and not compound figures.

Construction

As with all odd regular polygons and star polygons whose orders are not products of distinct

Fermat prime In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: 3, 5, ...

s, the regular hendecagrams cannot be constructed with compass and straightedge. However, describe folding patterns for making the hendecagrams , , and out of strips of paper.

Applications

Prism PRISM is a code name for a program under which the United States National Security Agency (NSA) collects internet communications from various U.S. internet companies. The program is also known by the SIGAD . PRISM collects stored internet ...

s over the hendecagrams and may be used to approximate the shape of

DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...

molecules. Fort Wood, now the base of the

Statue of Liberty The Statue of Liberty (''Liberty Enlightening the World''; ) is a colossal neoclassical sculpture on Liberty Island in New York Harbor, within New York City. The copper-clad statue, a gift to the United States from the people of French Thir ...

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

, is a

star fort A bastion fort or ''trace italienne'' (a phrase derived from non-standard French, meaning 'Italian outline') is a fortification in a style developed during the early modern period in response to the ascendancy of gunpowder weapons such as c ...

in the form of an irregular 11-point star. The

Topkapı Scroll The Topkapı Scroll () is a Timurid dynasty patterned scroll in the collection of the Topkapı Palace museum. The scroll is a valuable source of information, consisting of 114 patterns that may have been used both indirectly and directly by arch ...

contains images of an 11-pointed star

Girih ''Girih'' (, "knot", also written ''gereh'') are decorative Islamic geometric patterns used in architecture and handicraft objects, consisting of angled lines that form an interlaced strapwork pattern. ''Girih'' decoration is believed to have b ...

form used in

Islamic art Islamic art is a part of Islamic culture and encompasses the visual arts produced since the 7th century CE by people who lived within territories inhabited or ruled by Muslims, Muslim populations. Referring to characteristic traditions across ...

. The star in this scroll is not one of the regular forms of the hendecagram, but instead uses lines that connect the vertices of a

to nearly-opposite midpoints of the hendecagon's edges. 11-pointed star Girih patterns are also used on the exterior of the

Momine Khatun Mausoleum Momine Khatun Mausoleum () is a mausoleum, also known as the Atabek Dome, located in the city of Nakhchivan of the Nakhchivan Autonomous Republic in Azerbaijan. It was built in 1186 by the architect Ajami ibn Abubekr Nakhchivani. The ten-sided mau ...

; Eric Broug writes that its pattern "can be considered a high point in Islamic geometric design". An 11-point star-shaped cross-section was used in the

Space Shuttle Solid Rocket Booster The Space Shuttle Solid Rocket Booster (SRB) was the first solid-propellant rocket to be used for primary propulsion on a vehicle used for human spaceflight. A pair of them provided 85% of the Space Shuttle's thrust at liftoff and for the first ...

, for the core of the forward section of the rocket (the hollow space within which the fuel burns). This design provided more surface area and greater thrust in the earlier part of a launch, and a slower burn rate and reduced thrust after the points of the star were burned away, at approximately the same time as the rocket passed the

sound barrier The sound barrier or sonic barrier is the large increase in aerodynamic drag and other undesirable effects experienced by an aircraft or other object when it approaches the speed of sound. When aircraft first approached the speed of sound, th ...

References

External links

* {{Polygons 11 11 (number)

Regular hendecagrams

Construction

Applications

See also

References

External links