Editing Polygon (section)

==Naming==
The word ''polygon'' comes from [[Late Latin]] ''polygōnum'' (a noun), from [[Greek language|Greek]] πολύγωνον (''polygōnon/polugōnon''), noun use of neuter of πολύγωνος (''polygōnos/polugōnos'', the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a [[Greek language|Greek]]-derived [[numerical prefix]] with the suffix ''-gon'', e.g. ''[[pentagon]]'', ''[[dodecagon]]''. The [[triangle]], [[quadrilateral]] and [[nonagon]] are exceptions.

Beyond decagons (10-sided) and dodecagons (12-sided), mathematicians generally use numerical notation, for example 17-gon and 257-gon.<ref name=mathworld>Mathworld</ref>

Exceptions exist for side counts that are easily expressed in verbal form (e.g. 20 and 30), or are used by non-mathematicians. Some special polygons also have their own names; for example the [[regular polygon|regular]] [[star polygon|star]] [[pentagon]] is also known as the [[pentagram]].
{|class="wikitable"
|-
|+ '''Polygon names and miscellaneous properties'''
|-
!style="width:20em;" | Name
!style="width:2em;" | Sides
!style="width:auto;" | Properties
|-
|[[monogon]] || 1 || Not generally recognised as a polygon,<ref>Grunbaum, B.; "Are your polyhedra the same as my polyhedra", ''Discrete and computational geometry: the Goodman-Pollack Festschrift'', Ed. Aronov et al., Springer (2003), p. 464.</ref> although some disciplines such as graph theory sometimes use the term.<ref name="hm96">{{citation
 | last1 = Hass | first1 = Joel
 | last2 = Morgan | first2 = Frank
 | doi = 10.1090/S0002-9939-96-03492-2
 | issue = 12
 | journal = [[Proceedings of the American Mathematical Society]]
 | jstor = 2161556
 | mr = 1343696
 | pages = 3843–3850
 | title = Geodesic nets on the 2-sphere
 | volume = 124
 | date = 1996| doi-access = free}}</ref>
|-
|[[digon]] || 2 || Not generally recognised as a polygon in the Euclidean plane, although it can exist as a [[spherical polygon]].<ref>Coxeter, H.S.M.; ''Regular polytopes'', Dover Edition (1973), p. 4.</ref>
|-
|[[triangle]] (or trigon) || 3 || The simplest polygon which can exist in the Euclidean plane. Can [[triangular tiling|tile]] the plane.
|-
|[[quadrilateral]] (or tetragon) || 4 || The simplest polygon which can cross itself; the simplest polygon which can be concave; the simplest polygon which can be non-cyclic. Can [[square tiling|tile]] the plane.
|-
|[[pentagon]] || 5 || <ref name=namingpolygons/> The simplest polygon which can exist as a regular star. A star pentagon is known as a [[pentagram]] or pentacle.
|-
|[[hexagon]] || 6 || <ref name=namingpolygons/> Can [[hexagonal tiling|tile]] the plane.
|-
|[[heptagon]] (or septagon) || 7 || <ref name=namingpolygons/> The simplest polygon such that the regular form is not [[constructible polygon|constructible]] with [[compass and straightedge]]. However, it can be constructed using a [[neusis construction]].
|-
|[[octagon]] || 8 || <ref name=namingpolygons/>
|-
|[[nonagon]] (or enneagon) || 9 || <ref name=namingpolygons/>"Nonagon" mixes Latin [''novem'' = 9] with Greek; "enneagon" is pure Greek.
|-
|[[decagon]] || 10 || <ref name=namingpolygons/>
|-
|[[hendecagon]] (or undecagon) || 11 || <ref name=namingpolygons/> The simplest polygon such that the regular form cannot be constructed with compass, straightedge, and [[angle trisector]]. However, it can be constructed with neusis.<ref name=Benjamin/>
|-
|[[dodecagon]] (or duodecagon) || 12 || <ref name=namingpolygons/>
|-
|[[tridecagon]] (or triskaidecagon)|| 13 || <ref name=namingpolygons/>
|-
|[[tetradecagon]] (or tetrakaidecagon)|| 14 || <ref name=namingpolygons/>
|-
|[[pentadecagon]] (or pentakaidecagon) || 15 || <ref name=namingpolygons/>
|-
|[[hexadecagon]] (or hexakaidecagon) || 16 || <ref name=namingpolygons/>
|-
|[[heptadecagon]] (or heptakaidecagon)|| 17 || [[Constructible polygon]]<ref name=mathworld/>
|-
|[[octadecagon]] (or octakaidecagon)|| 18 || <ref name=namingpolygons/>
|-
|enneadecagon (or enneakaidecagon)|| 19 || <ref name=namingpolygons/>
|-
|[[icosagon]] || 20 || <ref name=namingpolygons/>
|-
|[[icositrigon]] (or icosikaitrigon) || 23 || The simplest polygon such that the regular form cannot be constructed with [[neusis construction|neusis]].<ref name=Baragar>Arthur Baragar (2002) Constructions Using a Compass and Twice-Notched Straightedge, The American Mathematical Monthly, 109:2, 151–164, {{doi|10.1080/00029890.2002.11919848}}</ref><ref name=Benjamin>{{cite journal
| last1=Benjamin | first1=Elliot
| last2=Snyder | first2=C
| title=On the construction of the regular hendecagon by marked ruler and compass
| journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]
| volume=156
| issue=3
| date=May 2014
| pages=409–424
| doi=10.1017/S0305004113000753| bibcode=2014MPCPS.156..409B
}}</ref>
|-
|[[icositetragon]] (or icosikaitetragon) || 24 || <ref name=namingpolygons/>
|-
|icosipentagon (or icosikaipentagon) || 25 || The simplest polygon such that it is not known if the regular form can be constructed with neusis or not.<ref name=Baragar/><ref name=Benjamin/>
|-
|[[triacontagon]] || 30 || <ref name=namingpolygons/>
|-
|tetracontagon (or tessaracontagon) || 40 || <ref name=namingpolygons/><ref name=Peirce/>
|-
|pentacontagon (or pentecontagon) || 50 || <ref name=namingpolygons/><ref name=Peirce>[https://books.google.com/books?id=wALvAAAAMAAJ&q=hebdomecontagon ''The New Elements of Mathematics: Algebra and Geometry''] by [[Charles Sanders Peirce]] (1976), p.298</ref>
|-
|hexacontagon (or hexecontagon) || 60 || <ref name=namingpolygons/><ref name=Peirce/>
|-
|heptacontagon (or hebdomecontagon) || 70 || <ref name=namingpolygons/><ref name=Peirce/>
|-
|octacontagon (or ogdoëcontagon) || 80 || <ref name=namingpolygons/><ref name=Peirce/>
|-
|enneacontagon (or enenecontagon) || 90 || <ref name=namingpolygons/><ref name=Peirce/>
|-
|hectogon (or hecatontagon)<ref name="drmath"/> || 100 || <ref name=namingpolygons>{{cite book |last=Salomon |first=David |title=The Computer Graphics Manual |url=https://books.google.com/books?id=DX4YstV76c4C&pg=PA90 |date=2011 |publisher=Springer Science & Business Media |isbn=978-0-85729-886-7 |pages=88–90 }}</ref>
|-
| [[257-gon]] <!--please don't add a rarely used English name such as "diacosipentecontaheptagon": it is too long--> || 257 || [[Constructible polygon]]<ref name=mathworld/>
|-
|[[chiliagon]] || 1000 || Philosophers including [[René Descartes]],<ref name=sepkoski>{{cite journal|last=Sepkoski|first=David|title=Nominalism and constructivism in seventeenth-century mathematical philosophy|journal=Historia Mathematica|year=2005|volume=32|pages=33–59|doi=10.1016/j.hm.2003.09.002|doi-access=free}}</ref> [[Immanuel Kant]],<ref>Gottfried Martin (1955), ''Kant's Metaphysics and Theory of Science'', Manchester University Press, [https://books.google.com/books?id=MDe9AAAAIAAJ&pg=PA22 p. 22.]</ref> [[David Hume]],<ref>David Hume, ''The Philosophical Works of David Hume'', Volume 1, Black and Tait, 1826, [https://books.google.com/books?id=4uQBAAAAcAAJ&pg=PA101 p. 101.]</ref> have used the chiliagon as an example in discussions.
|-
|[[myriagon]] || 10,000 || 
|-
| [[65537-gon]]<!--please don't add a rarely used English name such as "hexacismyripentacischilipentacosiatriacontaheptagon": it is too long--> || 65,537 || [[Constructible polygon]]<ref name=mathworld/>
|-
|[[megagon]]<ref>{{cite book |last=Gibilisco |first=Stan |title=Geometry demystified |year=2003 |publisher=McGraw-Hill |location=New York |isbn=978-0-07-141650-4 |edition=Online-Ausg. |url-access=registration |url=https://archive.org/details/geometrydemystif00stan }}</ref><ref name=Darling>Darling, David J., ''[https://books.google.com/books?id=0YiXM-x--4wC&dq=polygon+megagon&pg=PA249 The universal book of mathematics: from Abracadabra to Zeno's paradoxes]'', John Wiley & Sons, 2004. p. 249. {{isbn|0-471-27047-4}}.</ref><ref>Dugopolski, Mark, ''[https://books.google.com/books?id=l8tWAAAAYAAJ College Algebra and Trigonometry]'', 2nd ed, Addison-Wesley, 1999. p. 505. {{isbn|0-201-34712-1}}.</ref> || 1,000,000 || As with René Descartes's example of the chiliagon, the million-sided polygon has been used as an illustration of a well-defined concept that cannot be visualised.<ref>McCormick, John Francis, ''[https://books.google.com/books?id=KyFHAAAAIAAJ&q=%22million-sided+polygon%22 Scholastic Metaphysics]'', Loyola University Press, 1928, p. 18.</ref><ref>Merrill, John Calhoun and Odell, S. Jack, ''[https://books.google.com/books?id=_aNZAAAAMAAJ&q=%22million-sided+polygon%22 Philosophy and Journalism]'', Longman, 1983, p. 47, {{isbn|0-582-28157-1}}.</ref><ref>Hospers, John, ''[https://books.google.com/books?id=OVu0CORmhL4C&pg=PA56 An Introduction to Philosophical Analysis]'', 4th ed, Routledge, 1997, p. 56, {{isbn|0-415-15792-7}}.</ref><ref>Mandik, Pete, ''[https://books.google.com/books?id=5yHtsM-NToYC&pg=PA26 Key Terms in Philosophy of Mind]'', Continuum International Publishing Group, 2010, p. 26, {{isbn|1-84706-349-7}}.</ref><ref>Kenny, Anthony, ''[https://books.google.com/books?id=ehZGIy_ZYTgC&pg=PA124 The Rise of Modern Philosophy]'', Oxford University Press, 2006, p. 124, {{isbn|0-19-875277-6}}.</ref><ref>Balmes, James, ''[https://books.google.com/books?id=MrwKHqw06hMC&pg=PA27 Fundamental Philosophy, Vol II]'', Sadlier and Co., Boston, 1856, p. 27.</ref><ref>Potter, Vincent G., ''[https://books.google.com/books?id=SnO1FKnJui4C&pg=PA86 On Understanding Understanding: A Philosophy of Knowledge]'', 2nd ed, Fordham University Press, 1993, p. 86, {{isbn|0-8232-1486-9}}.</ref> The megagon is also used as an illustration of the convergence of [[regular polygon]]s to a circle.<ref>Russell, Bertrand, ''[https://books.google.com/books?id=Ey94E3sOMA0C&pg=PA202 History of Western Philosophy]'', reprint edition, Routledge, 2004, p. 202, {{isbn|0-415-32505-6}}.</ref>
|-
|[[apeirogon]] || ∞|| A degenerate polygon of infinitely many sides.
|}

To construct the name of a polygon with more than 20 and fewer than 100 edges, combine the prefixes as follows.<ref name=namingpolygons/> The "kai" term applies to 13-gons and higher and was used by [[Johannes Kepler|Kepler]], and advocated by [[John H. Conway]] for clarity of concatenated prefix numbers in the naming of [[quasiregular polyhedron|quasiregular polyhedra]],<ref name=drmath>{{cite web |title=Naming Polygons and Polyhedra |url=http://mathforum.org/dr.math/faq/faq.polygon.names.html |work=Ask Dr. Math |publisher=The Math Forum – Drexel University |access-date=3 May 2015}}</ref> though not all sources use it.
{|class="wikitable" style="vertical-align:center;"
|- style="text-align:center;"
!colspan="2" rowspan="2" | Tens
!''and''
!colspan="2" | Ones
!final suffix
|-
|rowspan="9" | -kai-
|1
| |-hena-
|rowspan=9 | -gon
|-
|20 || icosi- (icosa- when alone) || 2 || -di-
|-
|30 || triaconta- (or triconta-)|| 3 || -tri-
|-
|40 || tetraconta- (or tessaraconta-) || 4 || -tetra-
|-
|50 || pentaconta- (or penteconta-)|| 5 || -penta-
|-
|60 || hexaconta- (or hexeconta-) || 6 || -hexa-
|-
|70 || heptaconta- (or hebdomeconta-)|| 7 || -hepta-
|-
|80 || octaconta- (or ogdoëconta-)|| 8 || -octa-
|-
|90 || enneaconta- (or eneneconta-)|| 9 || -ennea-
|}