Asterisk

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Usage

Written text

• The asterisk is used to call out a footnote
  Footnote
  
  A footnote is a note of text placed at the bottom of a page in a book or document. The note comments on and/or may citation a reference for part of the main body of text....
  , especially when there is only one on the page. Less commonly, multiple asterisks are used to denote different footnotes on a page. (i.e., *, **, ***)
• Three spaced asterisks centered on a page may represent a jump to a different scene or thought. See Horizontal rule.
• One or more asterisks may be used to strike out portions of a word to avoid offending by using the full form of a profanity (f**k
  Fuck
  
  Fuck is an English word that, as a transitive verb, means "to have sexual intercourse with". It also has various metaphorical meanings:*The verb "to be fucked" can mean "to be cheated" ....
  ), to preserve anonymity (Peter J***), or to avoid profanation of a holy name (G*d
  God
  
  God is a deity in theism and deism religions and other belief systems, representing either the sole deity in monotheism, or a principal deity in polytheism....
  ).
• Asterisks are sometimes used instead of typographical bullets
  Bullet (typography)
  
  In typography, a bullet is a typographical symbol or glyph used to introduce items in a wiktionary:list, like below, also known as the point of a bullet:...
   to indicate items of a list.
• Colloquially, asterisks can be used to represent *emphasis* when italics
  Italic type
  
  In typography, italic type refers to cursive typefaces based on a stylized form of calligraphic handwriting. The influence from calligraphy can be seen in their usual slight slanting to the right....
   are not available (e.g. email).
• Asterisks are used to represent ratings of movies, restaurants, etc.: see Star (classification)
  Star (classification)
  
  Stars are often used as symbols for classification purposes. They are used by reviewers for ranking things such as movies, TV shows, restaurants, and hotels....
  .
• A group of three asterisks arranged in a triangular formation  is called an asterism
  Asterism (typography)
  
  In typography, an asterism is a rarely used symbol consisting of three asterisks placed in a triangle . It is used to call attention to a passage or to separate subchapters in a book....
  .

Linguistics

Historical linguistics

• *ainlif ? endleofan ? eleven

Generativist tradition in linguistics

• I'm not / *I amn't

• go *(to) the station
• go (*to) home

Music

• In musical notation the sign indicates when the sustain pedal
  Sustain pedal
  
  A sustain pedal or sustaining pedal is the most commonly used piano pedals in a modern piano. It is typically the rightmost of two or three pedals....
   of the piano should be lifted.

Computing

Computer science

Computer interfaces

Adding machines and printing calculators

Programming languages

• In some programming languages such as the C programming language
  C (programming language)
  
  C is a general-purpose computer programming language originally developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories to implement the Unix operating system....
  , the asterisk is used to dereference or to declare a pointer variable.
• In the Common Lisp
  Common Lisp
  
  Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in American National Standards Institute standard document Information Technology - Programming Language - Common Lisp, formerly X3.226-1994 ....
   programming language, the names of global variable
  Global variable
  
  In computer programming, a global variable is a variable that is accessible in every scope . Interaction mechanisms with global variables are called global environment mechanisms....
  s are conventionally set off with asterisks, *LIKE-THIS*.
• In the Fortran
  Fortran
  
  Fortran is a general-purpose programming language, procedural programming language, imperative programming language programming language that is especially suited to numerical analysis and scientific computing....
   programming language, and in some dialects of the Pascal programming language, a double asterisk is used to signify exponentiation
  Exponentiation
  
  Exponentiation is a mathematics operation , written 'an', involving two numbers, the base a and the exponent n....
  : 5**3 is 5*5*5 or 125.
• In the Perl programming language
  Perl
  
  In computer programming, Perl is a high-level programming language, List of programming languages by category, Interpreter , dynamic programming language....
  , the asterisk is used to refer to the typeglob of all variables with a given name.
• In the programming languages Ruby and Python
  Python (programming language)
  
  Python is a general-purpose high-level programming language. Its design philosophy emphasizes code readability. Python's core syntax and semantics are Minimalism , while the standard library is large and comprehensive....
  , * has two specific uses. Firstly, the unary * operator applied to a list object inside a function call will expand that list into the arguments of the function call. Secondly, a parameter preceded by * in the parameter list for a function will result in any extra parameters being aggregated into a tuple
  Tuple
  
  In mathematics, a tuple is a sequence of a specific number of values, called the components of the tuple. These components can be any kind of mathematical objects, where each component of a tuple is a value of a specified type....
   (Python) or array
  Array
  
  In computer science, an array is a data structure consisting of a group of element s that are accessed by index . In most programming languages each element has the same data type and the array occupies a contiguous area of computer memory....
   (Ruby).
• In the APL language, the asterisk represents the exponential
  Exponential
  
  Exponential may refer to any of several mathematical topics related to exponentiation, including:*Exponential function, also:**Matrix exponential, the matrix analogue to the above...
   and exponentiation
  Exponentiation
  
  Exponentiation is a mathematics operation , written 'an', involving two numbers, the base a and the exponent n....
   functions.

Mathematics

• The complex conjugate
  Complex conjugate
  
  In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. Thus, the conjugate of the complex number...
   of a complex number
  Complex number
  
  In mathematics, the complex numbers are an extension of the real numbers obtained by adjoining an imaginary unit, denoted i, which satisfies:...
   (though a more common notation is ).
• The free product
  Free product
  
  In mathematics, specifically group theory, the free product is an operation that takes two group G and H and constructs a new group G?*?H....
   of two groups
  Group (mathematics)
  
  In mathematics, a group is an algebraic structure consisting of a set together with an Binary operation that combines any two of its element to form a third element....
  .
• Infix notation
  Infix notation
  
  Infix notation is the common arithmetic and logical formula notation, in which operators are written infix-style between the operands they act on ....
   for an arbitrary binary operator.
• Convolution
  Convolution
  
  In mathematics and, in particular, functional analysis, convolution is a mathematical operator on two function s f and g, producing a third function that is typically viewed as a modified version of one of the original functions....
  , e.g. f g is a convolution of f with g.
• The multiplicative group of a ring
  Ring (mathematics)
  
  In mathematics, a ring is a type of algebraic structure. There is some variation among mathematicians as to exactly what properties a ring is required to have, as described in detail below....
  , especially when the ring is a field
  Field (mathematics)
  
  In abstract algebra, a field is an algebraic structure with notions of addition, subtraction, multiplication and division , satisfying certain axioms....
  . E.g.
• An arbitrary point in some set, for example in computing Riemann sums or when contracting a simply connected group to the singleton set .
• The dual space
  Dual space
  
  In mathematics, any vector space, V, has a corresponding dual vector space consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors which are studied in tensor algebra....
   of a vector space
  Vector space
  
  File:Vector addition ans scaling.pngA vector space is a mathematical structure formed by a collection of vectors: objects that may be Vector addition together and Scalar multiplication by numbers, called scalar s in this context....
   V is denoted V*.
• The combination of an indexed collection of objects into one example, e.g. the combination of all the cohomology groups
  Cohomology
  
  In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a cochain complex....
   H^k(X) into the cohomology ring
  Cohomology ring
  
  In mathematics, specifically algebraic topology, the cohomology ring of a topological space X is a ring formed from the cohomology groups of X together with the cup product serving as the ring multiplication....
   H*(X).
• The pushforward (differential) of a smooth map f between two smooth manifolds is denoted f.
• The Hodge dual
  Hodge dual
  
  In mathematics, the Hodge star operator or Hodge dual is a significant linear map introduced in general by W. V. D. Hodge. It is defined on the exterior algebra of a finite-dimensional orientation inner product space....
   operator on vector spaces .
• Hermitian adjoint
  Hermitian adjoint
  
  In mathematics, specifically in functional analysis, each linear operator on a Hilbert space has a corresponding adjoint operator.Adjoints of operators generalize conjugate transposes of square matrices to infinite-dimensional situations....
  
• In statistics, to denote critical points. z* and t* are given critical points for z-distributions and t-distributions, respectively.

Mathematical typography

Statistical results

Human genetics

• In human genetics, *
  * (haplogroup)
  
  In human genetics, Human mitochondrial DNA haplogroup and Human Y-chromosome DNA haplogroup are designated by letters of the alphabet. When a person takes a genealogical DNA test, the presence of an asterisk in their test result indicates that they are a member of a particular haplogroup, but not of a known subclade ....
   is used to denote that someone is a member of a haplogroup and not any of its subclades (see * (haplogroup)
  * (haplogroup)
  
  In human genetics, Human mitochondrial DNA haplogroup and Human Y-chromosome DNA haplogroup are designated by letters of the alphabet. When a person takes a genealogical DNA test, the presence of an asterisk in their test result indicates that they are a member of a particular haplogroup, but not of a known subclade ....
  ).

Telephony

E-mail, Usenet, IM

• In e-mail
  E-mail
  
  Electronic mail, often abbreviated as e-mail, email, E-Mail, or eMail, is any method of creating, transmitting, or storing primarily text-based human communications with digital communications systems....
   or other plain text
  Plain text
  
  In computing, plain text is a term used for an ordinary "unformatted" sequential file readable as textual material without much processing.The Character encoding has traditionally been either ASCII, one of its many derivatives such as ISO/IEC 646 etc., or sometimes EBCDIC....
   communications where multiple typefaces are not available, a word or phrase may be bracketed by asterisks *like this* to indicate emphasis
  Emphasis (typography)
  
  In typography, emphasis is the exaggeration of words in a text with a font in a different style from the rest of the text—to emphasise them....
   normally denoted by bold or italics
  Italic type
  
  In typography, italic type refers to cursive typefaces based on a stylized form of calligraphic handwriting. The influence from calligraphy can be seen in their usual slight slanting to the right....
  . Some writers make the distinction that asterisks denote bold text, while underscores, _like this_, denote italics. This follows the conventions of the auto-format features of word processors such as Microsoft Word.

• In informal written communications, particularly those via e-mail
  E-mail
  
  Electronic mail, often abbreviated as e-mail, email, E-Mail, or eMail, is any method of creating, transmitting, or storing primarily text-based human communications with digital communications systems....
  , instant messaging
  Instant messaging
  
  Instant messaging is a form of Real-time computing communication between two or more people based on typed text. The Written language is conveyed via devices connected over a network such as the Internet....
  , or BBS
  Internet forum
  
  An , or 'message board', is an online discussion site. It is the modern equivalent of a traditional bulletin board, and a technological evolution of the dialup bulletin board system....
  , asterisks are often used to bracket a predicate denoting the performance of an action, to indicate that the person typing is performing that action. Example: *writes an article*. Rather than a well-formed predicate in the third person singular, sometimes just the simplest form of the verb is used (e.g. *jump* or *glomp*), especially in text RPGs where unformatted text denotes speech.
• Asterisks can be used in place of applause in chatrooms and instant messaging
  Instant messaging
  
  Instant messaging is a form of Real-time computing communication between two or more people based on typed text. The Written language is conveyed via devices connected over a network such as the Internet....
  . For example:

Alice sings a song

Bob: Nice! ***********

• In chatrooms and instant messaging
  Instant messaging
  
  Instant messaging is a form of Real-time computing communication between two or more people based on typed text. The Written language is conveyed via devices connected over a network such as the Internet....
  , an asterisk is often, but not always, used to correct a typo. Usage varies on whether the asterisk comes before or after the correction. For example:

Alice: What do yuo think

Alice: *you

Bob: Wht,

Bob: Wha?*

Bob: What?**

• As in written text, asterisks may be used as bullets for list items.

• Asterisks (*****) are often used for censorship
  Censorship
  
  Censorship is the suppression of freedom of speech or deletion of communicative material which may be considered objectionable, harmful or sensitive, as determined by a censor....
  , especially on the internet, or in closed captioning
  Closed captioning
  
  Closed captioning is a term describing several systems developed to display Written language on a television or video Display device to provide additional or interpretive information to viewers who wish to access it....
   to remain faithful to the bleep censor
  Bleep censor
  
  A bleep censor is the replacement of verbal profanity with a beep , in television or radio. It is mainly used in the UK, the U.S., Canada, and Japan....
   in audiovisual media.

Cricket

• In cricket
  Cricket
  
  Cricket is a Bat-and-ball games team sport that originated in southern England. The earliest definite reference is dated 1598, and it is now played in more than 100 countries....
  , it signifies a total number of runs scored by a batsman without losing his wicket, e.g. 107* means '107 not out
  Not out
  
  In cricket, not out is a term used on scorecards to signify that a batsman has not been dismissal when the innings is finished. At least one batsman will be not out at the end of an innings ....
  '. When written before a player's name on a scorecard, it indicates the captain
  Captain (cricket)
  
  The captain of a cricket team is a individual who, during the course of a match, has several additional roles and responsibilities over and above those of a regular player....
  .

• It is also used on television when giving a career statistic during a match. For example, 47* in a number of matches column means that the current game is the player's 47th.

Economics

• In economics
  Economics
  
  File:Ballard Farmers' Market - vegetables.jpgEconomics is the Social sciences that studies the Production theory basics, Distribution , and Consumption of Good and Service ....
  , the use of an asterisk after a letter indicating a variable
  Variable
  
  A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e....
   such as price
  Price
  
  Price in economics and business is the result of an exchange and from that trade we assign a numerical monetary Value to a product , Service or asset....
  , output
  Output
  
  Output is the term denote either an exit or changes which exit a system and which activate/modify a process. It is an abstract concept, used in the model ing, system design and system exploitation....
  , or employment
  Employment
  
  Employment is a contract between two party , one being the #Employer and the other being the #Employee. An employee may be defined as: "A person in the Service of another under any contract of hire, express or implied, oral contract or written, where the employer has the power or right to control and Management the employee i...
   indicates that the variable is at its optimal level (that which is achieved in a perfect market situation). For instance, p* is the price level p when output y is at its corresponding optimal level of y*.

• Also in international economics asterisks are commonly used to denote economic variables in a foreign country. So for example "p" is the price of the home good and "p*" is the price of the foreign good etc.*

Education

• In the GCSE
  General Certificate of Secondary Education
  
  The General Certificate of Secondary Education is the name of an academic qualification awarded in a specified subject, generally taken in a number of subjects by students aged 13-16 in secondary education in England, Wales, and Northern Ireland....
   examination and PSLE
  Primary School Leaving Examination
  
  The Primary School Leaving Examination is a national examination taken by all students in Singapore near the end of their sixth year in primary education, which is also their last year in primary school before they leave for secondary education....
  , A* ("A-star") is a special top grade that is distinguished from grade A.

Games

• Certain categories of character types in role-playing game
  Role-playing game
  
  A role-playing game is a game in which the participants assume the roles of fictional characters. Participants determine the actions of their characters based on their characterization, and the actions succeed or fail according to a role-playing game system of rules and guidelines....
  s are called splats, and the game supplements describing them are called splatbook
  Splatbook
  
  Splatbooks are sourcebooks devoted to a particular facet, character class, or fictional Political faction in a role-playing game, providing additional background details and rules options....
  s. This usage originated with the shorthand "*book" for this type of supplement to various World of Darkness
  World of Darkness
  
  The World of Darkness is the name given to three related but distinct fictional universes. The first was conceived by Mark Rein-Hagen, while the second was designed by several people at White Wolf, which Rein-Hagen helped to found....
   games, such as Clanbook: Ventrue (for Vampire: The Masquerade
  Vampire: The Masquerade
  
  Created by Mark Rein?Hagen, Vampire: The Masquerade was the first of White Wolf, Inc. World of Darkness live-action role-playing game and role-playing games, based on the Storyteller System and centered around vampire s in a modern Goth subculture-Punk ideology world....
  ) or Tribebook: Black Furies (for Werewolf: The Apocalypse
  Werewolf: The Apocalypse
  
  Werewolf: The Apocalypse is a role-playing game and series of novels from the old World of Darkness line by White Wolf, Inc.. In this game, players take the role of werewolf known as Garou , warriors who are locked in a two-front war against the spiritual desolation of urban civilization and supernatural forces of corruption that...
  ), and this usage has spread to other games with similar character-type supplements. For example, Dungeons & Dragons
  Dungeons & Dragons
  
  Dungeons & Dragons is a fantasy role-playing game originally designed by Gary Gygax and Dave Arneson, and first published in 1974 by TSR, Inc....
   Third Edition has had several lines of splatbooks: the "X & Y" series including Sword & Fist and Tome & Blood prior to the "3.5" revision, the "Complete X" series including Complete Warrior and Complete Divine, and the "Races of X" series including Races of Stone and Races of the Wild.
• In many MUD
  MUD
  
  In Online game, a MUD , pronounced /m?d/, is a multi-user real-time virtual world described entirely in text. It combines elements of role-playing games, hack and slash, interactive fiction, and online chat....
  s and MOO
  Moo
  
  Moo or MOO can refer to a wide variety of things.* An onomatopoeia imitating the sound made by a cattle*Molly Moo-Cow, an animated character dating from the 1930s...
  s, as well as "male", "female", and other more esoteric genders, there is a gender called "splat", which uses an asterisk to replace the letters that differ in standard English gender pronouns. For example, h* is used rather than him or her. Also, asterisks are used to signify doing an action, for example, "*action*"
• Game show
  Game show
  
  A game show is a type of television program in which members of the public or celebrity, sometimes as part of a team, play a game which involves answering questions or solving problems for money and/or prizes....
   producer Mark Goodson
  Mark Goodson
  
  Mark Goodson was a successful United States television producer who specialized in game shows....
   used a six-pointed asterisk as his trademark. It is featured prominently on The Price Is Right, where the current set uses them on the floor (daytime shows only), Make Your Mark, Bonus Game, and starting in Season 36, the panels next to the Big Doors and the opening light box, and starting in Season 37, the Double Showcase Winner graphic and also the announcer's podium. This is often referred by host Drew Carey
  Drew Carey
  
  Drew Allison Carey is an United States comedian, actor, and game show host. After serving in the United States Marine Corps and making a name for himself in stand-up comedy, Carey eventually gained popularity starring on his own Situation comedy, The Drew Carey Show, and serving as host on the U.S....
   as "Goodson's Mark".

Baseball

• In recent years, the asterisk has come into use on scorecards to denote a "great defensive play."

Competitive sports and games

• In colloquial usage, an asterisk is used to indicate that a record
  World record
  
  A world record is the best performance in a certain discipline, often a sports event. Outside of conventional sports, world records can also be set in virtually anything that is measurable, but verifying these records is often very difficult....
   is somehow tainted by circumstances, which are putatively explained in a footnote supposedly referenced by the asterisk. This usage arose after the 1961 baseball season in which Roger Maris
  Roger Maris
  
  Roger Eugene Maris was an United States right fielder in Major League Baseball who is primarily remembered for breaking Babe Ruth's single-season home run record , in 1961 Major League Baseball season, a record that would stand for 37 years....
   of the New York Yankees
  New York Yankees
  
  The New York Yankees are a professional baseball based in the Borough of the Bronx, in New York City, New York and are a member of the American League East of Major League Baseball's American League....
   broke Babe Ruth
  Babe Ruth
  
  George Herman Ruth, Jr. , also popularly known as "Babe", "The Bambino", and "The Sultan of Swat", was an United States Major League Baseball baseball player from –....
  's 34-year-old single-season home run
  Home run
  
  In baseball, a home run is scored when the ball is hit in such a way that the batting is able to circle all the bases, ending at home plate and scoring run for himself and each baserunning who was already on base, with no error by the defensive team on the play....
   record. Because Ruth had amassed 60 home runs in a season with only 154 games, compared to Maris's 61 over 162 games, baseball commissioner Ford Frick
  Ford Frick
  
  Ford Christopher Frick, born in Wawaka, Indiana, was an United States sportswriter and executive who served as president of the National League from to and as the 3rd Baseball Commissioner from 1951 to ....
   announced that Maris' accomplishment would be recorded in the record books with an explanation (often referred to as "an asterisk" in the retelling). In fact, Major League Baseball
  Major League Baseball
  
  Major League Baseball is the highest level of play in American professional baseball. Specifically, Major League Baseball refers to the organization that operates the National League and the American League, by means of a joint organizational structure that has developed gradually between them since 1903 ....
   had no official record book at the time, but the stigma remained with Maris for many years, and the concept of a real or figurative asterisk denoting less-than-official records has become widely used in sports and other competitive endeavors. A 2001 TV movie about Maris' record-breaking season was called 61*
  61*
  
  61* is an American baseball movie, made for HBO, directed by Billy Crystal and written by Hank Steinberg. The film was first released on April 28, 2001....
   (pronounced sixty-one asterisk) in reference to the controversy.

Barry Bonds

Horse Racing

• In programs
  Event programme
  
  A program with respect to events such as theater performances, f?tes, sports events, etc., is a printed leaflet outlining the parts of the event scheduled to take place, principal performers and background information....
   distributed at race track
  Race track
  
  A race track is a purpose-built facility for racing of animals , automobiles, motorcycles or sportsperson. A race track may also feature grandstands or concourses....
  s, an asterisk next to a jockey
  Jockey
  
  In sport, a jockey is one who rides horses in horse racing or steeplechase racing, primarily as a profession. The word also applies to camel riders in camel racing; however, camel jockey profession is slowly being replaced by robotics....
  's name indicates that he or she is an apprentice
  Apprenticeship
  
  Apprenticeship is a system of training a new generation of practitioners of a skill. Apprentices or prot?g?s build their careers from apprenticeships....
  , and in many cases is allowed to ride at a slightly lesser weight than the other jockeys. Such a jockey is sometimes called a "bug boy." In past performances, an asterisk is also used to denote an approximate distance.

Pop Culture

• The Red Hot Chili Peppers
  Red Hot Chili Peppers
  
  Red Hot Chili Peppers are a Grammy Award-winning American Rock music band formed in Los Angeles, California, California, in 1983. For most of the band's existence, the members are vocalist Anthony Kiedis, guitarist John Frusciante, bassist Flea , and drummer Chad Smith....
   use an 8-pronged asterisk as their symbol.
• The popular Japanese Hip Hop/Rock group Orange Range
  Orange Range
  
  , stylized as ORANGE RANGE, is a 5-member Japanese alternative rock band , based in Okinawa. Formed in 2001, the band began with Spice Music and later signed with Sony Music Japan's gr8! records division in 2003....
   has a song titled "*~Asterisk
  Asterisk (Orange Range song)
  
  is the 10th single from Orange Range.It was used as the first opening to the anime Bleach . This song stayed on the top 20 in Japan for 22 weeks and spent most of it at number one....
  ", which is also the first opening theme song for the popular anime
  Anime
  
  is animation in Japan and considered to be "Japanese animation" in the rest of the world. Anime dates from about 1917.Anime, in addition to manga , is extremely popular in Japan and well known throughout the world....
   Bleach.
• The syndicated comic Doonesbury
  Doonesbury
  
  Doonesbury is a comic strip by Garry Trudeau that chronicles the adventures and lives of a vast array of different characters of different ages, professions, and backgrounds?from the President of the United States to the title character, Michael Doonesbury, now a middle-aged, remarried father....
   uses a floating asterisk (referring to the name "asterisk president") wearing a Roman helmet to represent George W. Bush
  George W. Bush
  
  George Walker Bush served as the List of Presidents of the United States President of the United States from 2001 to 2009. He was the 46th List of Governors of Texas from 1995 to 2000 before being United States presidential inauguration as President on January 20, 2001....
  .
• The independent Hip/Hop label QN5 uses an asterisk as the name of a compilation series of the label's work.
• The Matches
  The Matches
  
  The Matches are a Musical ensemble based in United States. The band formed in Oakland, California, in 1997, and currently comprises vocalist and rhythm guitarist Shawn Harris, lead guitarist and backup vocalist Jon Devoto, bassist and backup vocalist Dylan Rowe, and drummer Matt Whalen....
   make a reference to asterisks using the line "friends in quotes and girls with asterisks" in their song "Dog-Eared Page" from their first album, E. Von Dahl Killed the Locals
  E. Von Dahl Killed the Locals
  
  E. Von Dahl Killed the Locals is the debut album by The Matches, originally self-released in 2003 in music and later re-released on Epitaph Records in 2004 in music....
  .

Encodings

See also

• Arabic star
  Arabic star
  
  The Arabic star is a punctuation mark developed to be distinct from the asterisk . The asterisk had existed in feudal times, and the original shape of the asterisk was six-pointed, each point like a teardrop coming from the center....
  
• Star (glyph)
  Star (glyph)
  
  In typography, a star is any of a number of glyphs with a number of triangular points arrayed within an imaginary circle....