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Discrete dynamical system on polygons in the projective plane and on their moduli space
In mathematics, the pentagram map is a discrete dynamical system acting on polygons in the projective plane. It defines a new polygon whose vertices are
Pentagram_map
Five-pointed star polygon
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments
Pentagram
Topics referred to by the same term
horror movie Pentagram, a children's novel series by Anthony Horowitz The pentagram map, a geometrical construction defined for polygons "Pentagram" (Raised
Pentagram_(disambiguation)
American mathematician
been credited for developing the mathematical concept known as the pentagram map. In addition, he is author of a mathematics picture book for young children
Richard Schwartz (mathematician)
Richard_Schwartz_(mathematician)
International design studio
Pentagram is a design firm founded in 1972 by Alan Fletcher, Theo Crosby, Colin Forbes, Kenneth Grange and Mervyn Kurlansky in Notting Hill, London. The
Pentagram_(design_firm)
Class of commutative rings
finite-dimensional simple Lie algebras. Some dynamical systems, like the pentagram map, can be interpreted in terms of cluster mutations. This can be used
Cluster_algebra
Polygon that is the boundary of a convex set
redirect targets Implicit curve § Smooth approximation of convex polygons Pentagram map – Discrete dynamical system on polygons in the projective plane and
Convex_polygon
Shape with five sides
faces Golden ratio List of geometric shapes Pentagonal numbers Pentagram Pentagram map Pentastar, the Chrysler logo Pythagoras' theorem Trigonometric
Pentagon
Matrices satisfying a differential equation
defined for dynamical systems with discrete time, for instance the pentagram map. Hitchin, N. J. (1999). Integrable systems : twistors, loop groups,
Lax_pair
American graphic designer and painter
designer, painter, and design educator. She is a partner at the design firm Pentagram, which she joined in 1991. She began her career as an art director in
Paula_Scher
German mathematician (1833–1872)
surface Eigenvalues and eigenvectors Helmholtz equation Hyperboloid model Pentagram map Quaternary cubic "Prix". Comptes rendus hebdomadaires des séances de
Alfred_Clebsch
Property of certain dynamical systems
(or clock model) in 1- and 2-dimensions Quantum Heisenberg model The pentagram map and some of its generalisations Anti-integrability Hitchin system Integrable
Integrable_system
Israeli American mathematician
impossible," describing Ramsey theory, is attributed to him. Cyclic polytope Pentagram map, a related concept Wikiquote has quotations related to Theodore Motzkin
Theodore_Motzkin
British industrial designer (born 1970)
the industrial design consultancy Map Project Office, which he led until 2018 when he became a partner at Pentagram. During his career Marshall has won
Jon_Marshall
Type of motion that is approximately periodic
ISBN 978-981-4556-60-6. Quasiperiodicity Kolmogorov–Arnold–Moser theorem The pentagram map, a discrete dynamical system exhibiting a quasiperiodic motion
Quasiperiodic_motion
Yugoslav American mathematician (1929-2018)
uniform honeycomb Elongated square gyrobicupola Goldner–Harary graph Pentagram map Simplicial sphere Star coloring Star polygon Grünbaum's theorem Grünbaum–Rigby
Branko_Grünbaum
equal horizontal bands of green (top), yellow, and red, with a yellow pentagram and single yellow rays emanating from the angles between the points on
List of national flags of sovereign states
List_of_national_flags_of_sovereign_states
Kepler–Poinsot polyhedron
regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex. It shares the same vertex arrangement as the convex
Small_stellated_dodecahedron
First-person shooter
soundtrack; shortly after the game's release in May 2016, players discovered pentagrams and the number "666" hidden in the track "Cyberdemon" via spectrogram
Doom_(2016_video_game)
Cubic graph with 10 vertices and 15 edges
The most common and symmetric plane drawing of the Petersen graph, as a pentagram within a pentagon, has five crossings. However, this is not the best drawing
Petersen_graph
Plane figure bounded by line segments
the vertices) can be any integer multiple d of 360°, e.g. 720° for a pentagram and 0° for an angular "eight" or antiparallelogram, where d is the density
Polygon
discovery, which they soon learn could be another victim of the long-lost Pentagram killer. The case takes a turn when they learn that the victim was disliked
List_of_The_Rookie_episodes
Biblical sea monster
Baphomet to represent Leviathan. Starting from the lowest point of the pentagram, and reading counter-clockwise, the word reads "לויתן": (Nun, Tav, Yod
Leviathan
Commercial offices in Abu Dhabi, United Arab Emirates
Image of a human body in a pentagram from Heinrich Cornelius Agrippa's Libri tres de occulta Philosophia. If the inner circle were the circumference of
Aldar_Headquarters_building
Flag of Eritrea – the emblem of Eritrea Flag of Ethiopia – the rayed pentagram emblem of Ethiopia Flag of French Polynesia – the French Polynesia seal
List of national flags by design
List_of_national_flags_by_design
Observation tower in Seattle, Washington, U.S.
Fair would begin. The Needle was privately financed and built by the Pentagram Corporation, consisting of Bagley Wright, contractor Howard S. Wright
Space_Needle
American brewery
Hopped Cask India Pale Ale Tea Bagged Bender Dry Hopped Cask Brown Ale Pentagram Wine Barrel-Aged Brett Dark Ale One Time Release beers Sausage Fest Smoked
Surly_Brewing_Company
American supernatural thriller television series
son Wyatt, who vanished several months earlier and left the mark of a pentagram in his room. Kristen's daughters help her deduce that Wyatt is a victim
Evil_(American_TV_series)
Submarine April 14, 2023 (2023-04-14) Detective Conan: The Million-dollar Pentagram April 12, 2024 (2024-04-12) Detective Conan: One-eyed Flashback April 18
List of films based on television programs
List_of_films_based_on_television_programs
2006 Thornton Heath, Croydon, England Heart attack Vince McAllister Pentagram 51 May 26, 2006 San Francisco Bay Area, California, U.S. Neck cancer Rocío
List of 2000s deaths in popular music
List_of_2000s_deaths_in_popular_music
American multinational foodservice retailer
of their Times Square location the same year. As part of the changes, Pentagram design studios were hired to help construct a new public visual identity
Ruby_Tuesday_(restaurant)
U.S. state
Jim (April 11, 2019). "Severe weather awareness for spring, summer". Pentagram. Retrieved May 29, 2020. "Annual tornado drill in Virginia will be held
Virginia
Russian political philosopher (born 1962)
things esoteric – mysticism, hypnotism, Ouija boards, Sufism, trances, pentagrams and so forth. In the group, he was known for his embrace of Nazism which
Aleksandr_Dugin
Flags arranged by design
(1967–1977) Flag of the East Turkestan independence movement Flag of Ethiopia (pentagram) Flag of Europe Flag of the European Coal and Steel Community Flag of
List_of_flags_by_design
Flag of Morocco See also: List of Moroccan flags Red with a dark green pentagram in its center. 1983–present Flag of Mozambique See also: List of Mozambican
Flags_of_Africa
into the key hole. Colt also built a railroad of iron, in the shape of a pentagram with a church at each of the points, around the devil's gate to further
List of Supernatural and The Winchesters characters
List_of_Supernatural_and_The_Winchesters_characters
Pentagon with all sides equal but the angles may not be equal
intersected by others. A common example of this type of pentagon is the pentagram. A condition for a pentagon to be stellated, or self-intersecting, is
Equilateral_pentagon
German polymath and scholar (1777–1855)
concerned with John Napier's "Pentagramma mirificum" – a certain spherical pentagram – for several decades; he approached it from various points of view, and
Carl_Friedrich_Gauss
Football stadium in Beşiktaş, Istanbul, Turkey
to Manowar, Rammstein, Alice in Chains, Accept, Stone Sour, Volbeat, Pentagram and Hayko Cepkin. Rihanna performed as part of the Diamonds World Tour
Beşiktaş_Stadium
Series of rhythm video games
music. Activision used the services of the Pentagram design studio to refashion the game's logo. Pentagram developed a new font, removing some of the
Guitar_Hero
Variety of rituals of magic
Banishing Ritual of the Pentagram. Crowley describes banishing in his Magick, Book 4 (ch.13): [...] in the banishing ritual of the pentagram we not only command
Ceremonial_magic
American television series
demon breakouts and sacrifices to find that they are forming a Satanic pentagram in shape. In flashbacks, Midge struggles to pay for her son, Benji's,
The_Bondsman
Genre of rock music
Sword's Age of Winters (2006) drew heavily on the work of Black Sabbath and Pentagram, Witchcraft added elements of folk rock and psychedelic rock, and Wolfmother's
Heavy_metal_music
Figure in Abrahamic religions
The inverted pentagram, along with Baphomet, is the most notable and widespread symbol of Satanism.
Satan
Occult symbols Ouroboros Papal cross Patriarchal cross Pearl Pentacle Pentagram Quincunx Raven banner Red Cross Red Rose of Lancaster Rod of Asclepius
List_of_symbols
symbol {}. Polygon Equilateral Cyclic polygon Convex polygon Star polygon Pentagram Regular polygon Equilateral triangle Simplex Square Cross-polytope Hypercube
List_of_mathematical_shapes
Joint base of US military near Arlington, Virginia
named the Cody Child Development Center (CDC), is located here. The Pentagram is written and produced here. It is a weekly newspaper that is delivered
Joint Base Myer–Henderson Hall
Joint_Base_Myer–Henderson_Hall
Polyhedron with regular congruent polygons as faces
Regular star polygons such as the pentagram (star pentagon) were also known to the ancient Greeks – the pentagram was used by the Pythagoreans as their
Regular_polyhedron
Airline of the United States
10, 2022. Retrieved January 4, 2013. "Fifteen Years of Flying United". Pentagram.com. Archived from the original on May 3, 2014. Retrieved April 27, 2014
United_Airlines
Historic building in London, England
Unilever House: Towards A New Ornament. In Pentagram Partners (Author), Delphine Hirasuna (Editor): Pentagram Papers. Chronicle Books, 2006, ISBN 978-0-8118-5563-1
Unilever_House
2012 Microsoft operating system version
February 17, 2012, Microsoft unveiled a new logo for Windows 8. Designed by Pentagram partner Paula Scher, the Windows logo was changed to resemble a set of
Windows_8
Second planet from the Sun
gravity simulation of the pentagram that the orbit of Venus traces when Earth is held fixed at the centre of the coordinate system Map-a-Planet: Venus by the
Venus
English typographer (born 1940)
London. In 1973 Kitching began his own design practice in London with Pentagram co-founder Colin Forbes. In 1977 he partnered with Derek Birdsall and
Alan Kitching (typographic artist)
Alan_Kitching_(typographic_artist)
Railway terminal in Manhattan, New York
of a railroad spike. The 2017 logo succeeded one created by the firm Pentagram for the terminal's centennial in 2013. It depicted the Main Concourse's
Grand_Central_Terminal
7-regular undirected graph with 50 nodes and 175 edges
constructions of the Hoffman–Singleton graph. Take five pentagons Ph and five pentagrams Qi . Join vertex j of Ph to vertex h · i + j of Qi (all indices are modulo
Hoffman–Singleton_graph
Elite US Army light infantry unit
on 1 October 2014. Retrieved 21 November 2012. "Adopting the Beret". Pentagram [newspaper]. Army News Service. 23 March 2001. Archived from the original
75th_Ranger_Regiment
1925 German-language book by Thea von Harbou
instead. The Magician’s House is the oldest house in Metropolis, with a red pentagram set into every door. The Magician vanished many years past, but the house
Metropolis_(novel)
1996 video game
recurring theme of hellish and satanic imagery reminiscent of Doom (such as pentagrams and images of demons on the walls). The game's setting is inspired by
Quake_(video_game)
Lattice group in Euclidean space whose points are integer n-tuples
Approximations of regular pentagrams with vertices on a square lattice with coordinates indicated
Integer_lattice
Church in Bedfordshire, England
Lancashire, symbols painted on the porch of a church in Bramber, Sussex, and a pentagram and a sheep's heart pierced with thirteen thorns in St Clement's in Leigh-on-Sea
St_Mary's_Church,_Clophill
1998 video game
Rebus, primarily within the areas of Cross Land, Idorus, Nordia, and Pentagram. The game is broken into 36 chapters: 18 in Toxa's scenario and 18 in
Kartia:_The_Word_of_Fate
Net used for fishing
bark and stones Cork float of a fisher net engraved with a protective pentagram, Hvide Sande, Denmark Dog conches are used to weigh down fishing nets
Fishing_net
commissioned Pentagram to update the brand. Pentagram soon decided to keep the "tulip", in view of its strong brand-recognition. Pentagram designed a new
History_of_United_Airlines
modern exploration of the planet". Map Project Office. Map Project Office. Retrieved 28 April 2016. Banks, Tom. "Pentagram brand for SAM "never stands still""
Sam_Labs
American fast casual burger restaurant
ISBN 978-1-62585-717-0. Retrieved November 14, 2017. "Shake Shack — Story". Pentagram. Archived from the original on August 4, 2020. Retrieved February 28,
Shake_Shack
National cultural center of the United States
Retrieved January 28, 2024. "'Art and Ideals: President John F. Kennedy'". Pentagram. Archived from the original on January 28, 2024. Retrieved January 28
Kennedy_Center
Covariance and correlation
Scaled correlation Spectral density Wiener–Khinchin theorem Bracewell, R. "Pentagram Notation for Cross Correlation." The Fourier Transform and Its Applications
Cross-correlation
Deity in Wicca and some forms of Neopaganism
and the two aspects of the Horned god are sometimes mapped on to the five points of the Pentagram or Pentacle, although which points correspond to which
Horned_God
2016 video game
upstairs. The player then finds out that the Talking Tattletails have made a pentagram out of the Christmas lights with the VHS tape in the middle, and have
Tattletail
American soldier (1887–1964)
1993". Retrieved October 21, 2017. Ford, Spc. Keisha (May 5, 2000). "The Pentagram: U.S. Postal Service salutes four American war heroes". Center of Military
Alvin_York
Building in Split, Croatia
of the marble rood screens. The second rood screen is decorated with pentagram with flowers and birds inside a star that is surrounded by a wreath which
Temple_of_Jupiter,_Split
Annual Indian music festival
modeled after the Glastonbury Festival in Britain where he had taken Pentagram in 2005. In 2009 he met UK music manager Stephen Budd in Mumbai and they
NH7_Weekender
Culture heritage estate near Sintra, Portugal
the Portuguese discoveries and the Order of Christ Cross, surrounded by pentagrams. Despite its relatively small size, the chapel has several floors. The
Quinta_da_Regaleira
Retrieved January 5, 2025. LaPierre, Megan (September 13, 2024). "David Gray Maps Out 2025 World Tour". Exclaim!. Retrieved September 14, 2024. Carter, Emily
List_of_2025_albums
2019 mass shooting in Colorado, U.S.
hand-painted graffiti that read "Fuck society" as well as "666" and a pentagram. One student was killed and eight others were injured in the shooting;
STEM School Highlands Ranch shooting
STEM_School_Highlands_Ranch_shooting
Solid with twenty equal triangular faces
a regular icosahedron. These new faces intersect each other, making a pentagram as the vertex figure. The triakis icosahedron is a Catalan solid constructed
Regular_icosahedron
2019 Doom episode
the previous episodes, with a liberal placement of lava, floor cracks, pentagrams, and other elements of a more hellish atmosphere. I wanted the levels
Sigil_(video_game_mod)
arms) Morocco 1915 1915 1915 (the Seal of Solomon is replaced by a green pentagram) Thailand 1917 1917 30 September 2017 (colours standardized) Austria
List of sovereign states by date of current flag adoption
List_of_sovereign_states_by_date_of_current_flag_adoption
Jewish kingdom in the southern Levant (140–37 BC)
in archaic paleo-Hebrew script arranged between the outer points of a pentagram. Like the revived script on later Hasmonean coinage, these administrative
Hasmonean_Judea
B-A-D-G-b-E Claimed to have been invented by guitarist Victor Griffin of Pentagram (who tunes it 1/2 step down). Also used in the songs "Rusty Cage" "Holy
List_of_guitar_tunings
Geometric model of the planar projection of the physical universe
on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme
Euclidean_plane
Art form on the medium of LSD blotter paper
often incorporates religious, mystical and occult symbology, such as pentagrams, a Tetragrammaton, Knights of Malta shields, the Giza pyramids, and UFOs
Blotter_art
1995 role-playing video game
black character in the game: the star mark on his forehead represented a pentagram, which resulted in him getting the production nickname "shooting star"
Shin Megami Tensei: Devil Summoner
Shin_Megami_Tensei:_Devil_Summoner
Moe released their first studio album in five years, Circle of Giants. Pentagram released their first studio album in ten years, Lightning in a Bottle
2025_in_American_music
2012 studio album by Cancer Bats
venue locations for the mini-tour, dubbed the Pentagram Tour, form a pentagram shape when seen on a map. About the unique structure of the tour, Cormier
Dead_Set_on_Living
on the town of Lancaster. Pentagram City, Pride Ring Hazbin Hotel SpindleHorse Toons, A24 Pentagram City (or The Pentagram) is a massive urbanized city
List of fictional towns in animation
List_of_fictional_towns_in_animation
2016 box set by Pink Floyd
Lana Topham – curator, producer and archivist for The Early Years films. Pentagram – package design. John Whiteley – 1960s psychedelic paper design. Peter
The_Early_Years_1965–1972
Unicode block
Symbols and Pictographs, Symbols and Pictographs Extended-A and Transport and Map Symbols. In Unicode 1.0 (1991) the same block was named Miscellaneous Dingbats
Miscellaneous_Symbols
Season 40 of the television series
fortieth anniversary, SNL introduced a new logo created by design firm Pentagram. Prior to the start of the season, five new writers were hired: Alison
Saturday_Night_Live_season_40
Japanese video game developer and publisher
3, PlayStation Vita, Xbox 360) Puella Magi Madoka Magica: The Battle Pentagram (PlayStation Vita) 2014 A-Train 3D: City Simulator (Nintendo 3DS) 2015
Artdink
Residential area of north west London, England
of Canterbury. Churchfields, Harrow on the Hill, centre of the Harrow Pentagram: Hergae Mound Oak trees leading from the Yew tree grove in Churchfields
Harrow_on_the_Hill
Office skyscraper in Manhattan, New York
Edward Larrabee Barnes, the building's original designer. Advertising firm Pentagram assisted with the graphic design of the way-finding information. 599 Lexington
599_Lexington_Avenue
District of Karlsruhe
another nature reserve in Knielingen. Knielingen has a black "Drudenfuß" (Pentagram) in its coat of arms. The coat of arms colors black and gold were adopted
Knielingen
Flat-sided three-dimensional shape
imaginative etchings. Johannes Kepler (1571–1630) used star polygons, typically pentagrams, to build star polyhedra. Some of these figures may have been discovered
Polyhedron
Rosicrucian esoteric Christian order
Scotland, which are under the jurisdiction of the SRIA's sister societies. A map of all SRIA colleges has been published on the official SRIA's official website
Societas Rosicruciana in Anglia
Societas_Rosicruciana_in_Anglia
1991 video game
stabbing, Bonds links it to an unsolved murder, in which the victim had a pentagram carved into their body post mortem. With the help of a witness, Bonds
Police_Quest_III:_The_Kindred
English architect
argument includes the idea that the locations of the churches form a pentagram with ritual significance. In Towcester, Northamptonshire Nicholas Hawksmoor
Nicholas_Hawksmoor
Performing arts centre in London, England
In the mid-1990s, a cosmetic improvement scheme by Theo Crosby, of the Pentagram design studio, added statues and decorative features reminiscent of the
Barbican_Centre
Triangular arrangement joining three rail lines
used a number of "inversion stars" for turning locomotives. This uses a pentagram layout, requiring four movements and five turnouts to reverse. It allows
Wye_(rail)
Japanese manga series
1991 (1991-09-22) Honmaru wants to go on a date with Iyona in autumn. Ria puts a pentagram sticker on Honmaru and says it will grant him one wish. Honmaru goes to
Magical_Taruruto
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