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29:
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447:
777:
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Symmetries of a regular enneagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices, and purple mirrors are drawn through edge. Gyration orders are given in the center.
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The regular enneagon can tessellate the euclidean tiling with gaps. These gaps can be filled with regular hexagons and isosceles triangles. In the notation of
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1038:
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1014:. It refers to both an attendee at a party at which "everybody in the party is a many-sided polygon" and a dance they perform at this party.
455:
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1023:
1020:'s logo is also a version of a nonagon, being a nine-pointed star made of three triangles, referring to the nine members.
1235:
915:
when reflection lines path through both edges and vertices. Cyclic symmetries in the middle column are labeled as
295:(εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct, though less common than "nonagon".
1054:
1030:', the album art featuring a nonagonal complete graph. The album consists of nine songs and repeats cyclically.
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Nonagon, an animation from a neusis construction based on the angle trisection 120° by means of the
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Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the
634:
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this tiling is called H(*;3;*;) with H representing *632 hexagonal symmetry in the plane.
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903:. The dihedral symmetries are divided depending on whether they pass through vertices (
892:
1183:(Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)
799:), there are very old methods of construction that produce very close approximations.
442:{\displaystyle A={\frac {9}{4}}a^{2}\cot {\frac {\pi }{9}}=(9/2)ar=9r^{2}\tan(\pi /9)}
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63:
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1151:"KLASSISCHE PROBLEME DES GRIECHISCHENALTERTUMS IM MATHEMATIKUNTERRICHT DER OBERSTUFE"
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Springer-Verlag New York, Inc. 1st edition 1986, retrieved on 11 December 2015.
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labels these by a letter and group order. Full symmetry of the regular form is
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772:{\displaystyle R={\sqrt {(a/2)^{2}+r^{2}}}=r\sec(\pi /9)=(a/2)\csc(\pi /9).}
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These 6 symmetries can be seen in 6 distinct symmetries on the enneagon.
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1160:. Bund der Freien Waldorfschulen Deutschlands. pp. 234–237.
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538:{\displaystyle =(9/2)R^{2}\sin(2\pi /9)\simeq 6.18182\,a^{2},}
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1137:"Episodes in the Mathematics of Medieval Islam", p. 82 - 85
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with all 36 edges connected. This graph also represents an
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have a song entitled "Nonagon" on their children's album
864:, order 18. There are 2 subgroup dihedral symmetries: Dih
236:
197:
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Nonagon, a neusis construction based on a hexagon with
926:
subgroup has no degrees of freedom but can be seen as
318:
of 140°. The area of a regular nonagon of side length
646:
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Trisection of the angle 60°, Proximity construction
221:
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441:
1757:
1110:
831:trisection of the angle according to Archimedes
284:and in English from the 17th century. The name
795:(as 9 = 3, which is not a product of distinct
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1758:
974:of the 9 vertices and 36 edges of the
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1024:King Gizzard & the Lizard Wizard
1243:
1175:, (2008) The Symmetries of Things,
1149:Ernst Bindel, Helmut von Kügelgen.
919:for their central gyration orders.
619:{\displaystyle r=(a/2)\cot(\pi /9)}
13:
787:Although a regular nonagon is not
298:
14:
1787:
1201:
802:It can be also constructed using
1057:, are required to be nonagonal.
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217:
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89:
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1766:Polygons by the number of sides
1171:John H. Conway, Heidi Burgiel,
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806:, or by allowing the use of an
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1210:(with interactive animation)
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33:A regular enneagon (nonagon)
7:
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899:and no symmetry is labeled
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10:
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1162:Retrieved on 14 July 2019.
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560:of the regular nonagon is
22:Regular enneagon (nonagon)
1652:
1598:
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1064:is an irregular nonagon.
954:
911:for perpendiculars), and
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1055:Baháʼí Houses of Worship
907:for diagonal) or edges (
793:compass and straightedge
1208:Properties of a Nonagon
972:orthographic projection
821:, at the end 10 s break
74:Coxeter–Dynkin diagrams
1041:
1026:have an album titled '
1000:Pop culture references
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833:
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1173:Chaim Goodman-Strauss
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847:
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633:is the radius of its
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16:Shape with nine sides
1469:Nonagon/Enneagon (9)
1399:Tangential trapezoid
1006:They Might Be Giants
966:is often drawn as a
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635:circumscribed circle
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456:
329:
1581:Megagon (1,000,000)
1349:Isosceles trapezoid
1551:Icositetragon (24)
1113:Weisstein, Eric W.
1042:
1011:Here Come the 123s
850:
834:
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310:is represented by
250:) is a nine-sided
1776:Elementary shapes
1753:
1752:
1594:
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1571:Myriagon (10,000)
1556:Triacontagon (30)
1520:Heptadecagon (17)
1510:Pentadecagon (15)
1505:Tetradecagon (14)
1444:Quadrilateral (4)
1314:Antiparallelogram
1181:978-1-56881-220-5
997:
996:
692:
552:where the radius
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1566:Chiliagon (1000)
1546:Icositrigon (23)
1525:Octadecagon (18)
1515:Hexadecagon (16)
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1135:J. L. Berggren,
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1062:U.S. Steel Tower
1028:Nonagon Infinity
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968:regular enneagon
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854:regular enneagon
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558:inscribed circle
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1500:Tridecagon (13)
1490:Hendecagon (11)
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1379:Right trapezoid
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1158:Erziehungskunst
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1049:Temples of the
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808:angle trisector
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316:internal angles
312:Schläfli symbol
301:
299:Regular nonagon
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64:Schläfli symbol
43:Regular polygon
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1495:Dodecagon (12)
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1202:External links
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1070:in Lithuania.
1068:Garsų Gaudyklė
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1039:Garsų Gaudyklė
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964:complete graph
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1685:Infinite skew
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1586:Apeirogon (∞)
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1530:Icosagon (20)
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1364:Parallelogram
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1359:Orthodiagonal
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1339:Ex-tangential
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876:symmetries: Z
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797:Fermat primes
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789:constructible
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1539:>20 sides
1474:Decagon (10)
1468:
1459:Heptagon (7)
1449:Pentagon (5)
1439:Triangle (3)
1334:Equidiagonal
1188:
1167:
1157:
1144:
1131:
1119:
1106:
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1059:
1051:Baháʼí Faith
1048:
1045:Architecture
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874:cyclic group
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786:
783:Construction
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322:is given by
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314:{9} and has
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277:
276:, "ninth" +
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158:Dual polygon
111:), order 2×9
1735:Star-shaped
1710:Rectilinear
1680:Equilateral
1675:Equiangular
1639:Hendecagram
1483:11–20 sides
1464:Octagon (8)
1454:Hexagon (6)
1429:Monogon (1)
1271:Equilateral
893:John Conway
288:comes from
143:equilateral
1771:9 (number)
1760:Categories
1740:Tangential
1644:Dodecagram
1422:1–10 sides
1413:By number
1394:Tangential
1374:Right kite
1098:References
1088:(nonagram)
1076:in Italy.
629:and where
293:enneagonon
254:or 9-gon.
131:Properties
1720:Reinhardt
1629:Enneagram
1619:Heptagram
1609:Pentagram
1576:65537-gon
1434:Digon (2)
1404:Trapezoid
1369:Rectangle
1319:Bicentric
1281:Isosceles
1258:Triangles
1121:MathWorld
1116:"Nonagon"
1086:Enneagram
1074:Palmanova
1053:, called
991:8-simplex
976:8-simplex
753:π
747:
710:π
704:
603:π
597:
516:≃
502:π
493:
426:π
420:
367:π
362:
257:The name
1695:Isotoxal
1690:Isogonal
1634:Decagram
1624:Octagram
1614:Hexagram
1415:of sides
1344:Harmonic
1245:Polygons
1193:TMBW.net
1080:See also
1018:Slipknot
872:, and 3
862:symmetry
840:Symmetry
819:Tomahawk
286:enneagon
282:nonogone
213:enneagon
170:geometry
151:isotoxal
147:isogonal
105:Dihedral
54:vertices
1715:Regular
1660:Concave
1653:Classes
1561:257-gon
1384:Rhombus
1324:Crossed
934:Tilings
884:, and Z
868:and Dih
556:of the
519:6.18182
308:nonagon
306:regular
268:, from
259:nonagon
252:polygon
174:nonagon
121:degrees
1725:Simple
1670:Cyclic
1665:Convex
1389:Square
1329:Cyclic
1291:Obtuse
1286:Kepler
1179:
955:Graphs
804:neusis
263:prefix
139:cyclic
135:Convex
1700:Magic
1296:Right
1276:Ideal
1266:Acute
1154:(PDF)
993:(8D)
959:The K
791:with
290:Greek
278:gonon
274:nonus
270:Latin
261:is a
211:) or
50:Edges
1730:Skew
1354:Kite
1249:List
1177:ISBN
1060:The
856:has
852:The
172:, a
162:Self
126:140°
52:and
39:Type
897:r18
880:, Z
858:Dih
744:csc
701:sec
594:cot
490:sin
417:tan
359:cot
168:In
68:{9}
1762::
1156:.
1118:.
978:.
930:.
924:g9
901:a1
888:.
810:.
637::
303:A
149:,
145:,
141:,
137:,
107:(D
1251:)
1247:(
1237:e
1230:t
1223:v
1124:.
961:9
917:g
913:i
909:p
905:d
886:1
882:3
878:9
870:1
866:3
860:9
767:.
764:)
761:9
757:/
750:(
741:)
738:2
734:/
730:a
727:(
724:=
721:)
718:9
714:/
707:(
698:r
695:=
688:2
684:r
680:+
675:2
671:)
667:2
663:/
659:a
656:(
651:=
648:R
631:R
614:)
611:9
607:/
600:(
591:)
588:2
584:/
580:a
577:(
574:=
571:r
554:r
533:,
528:2
524:a
513:)
510:9
506:/
499:2
496:(
485:2
481:R
477:)
474:2
470:/
466:9
463:(
460:=
437:)
434:9
430:/
423:(
412:2
408:r
404:9
401:=
398:r
395:a
392:)
389:2
385:/
381:9
378:(
375:=
370:9
354:2
350:a
344:4
341:9
336:=
333:A
320:a
272:(
246:/
243:n
240:ɒ
237:ɡ
234:ə
231:i
228:n
225:ɛ
222:ˈ
219:/
215:(
207:/
204:n
201:ɒ
198:ɡ
195:ə
192:n
189:ɒ
186:n
183:ˈ
180:/
176:(
123:)
119:(
109:9
58:9
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