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{{Short description|Integer number 6}}
{{Hatnote|This article is about the number. For the years, see 6 BC and AD 6. For other uses, see 6 (disambiguation) and Number Six (disambiguation).}}
{{Infobox number
|number=6
|numeral=[[Senary|senary]]
|divisor=1, 2, 3, 6
|roman =VI, vi, ↅ
|greek prefix=hexa-/hex-
|latin prefix=sexa-/sex-
|lang1=[[Greek numerals|Greek]]
|lang1 symbol=στ (or ΣΤ or ς)
 Kurdish, [[Social:Sindhi language|Sindhi]], Urdu
|lang2 symbol={{resize|150%|٦}}
|lang3=[[Social:Persian language|Persian]]
|lang3 symbol={{resize|150%|۶}}
|lang4=Amharic
|lang4 symbol=፮
|lang5=[[Social:Bengali language|Bengali]]
|lang5 symbol={{resize|150%|৬}}
|lang6=Chinese numeral
|lang6 symbol=六，陸
|lang7=Devanāgarī
|lang7 symbol={{resize|150%|६}}
|lang8=Gujarati
|lang8 symbol={{resize|150%|૬}}
|lang9=Hebrew
|lang9 symbol={{resize|150%|ו}}
|lang10=[[Khmer numerals|Khmer]]
|lang10 symbol=៦
|lang11=[[Thai numerals|Thai]]
|lang11 symbol=๖
|lang12=[[Social:Telugu language|Telugu]]
|lang12 symbol=౬
|lang13=[[Tamil numerals|Tamil]]
|lang13 symbol=௬
|lang14=Saraiki
|lang14 symbol={{resize|150%|٦}}
|lang15=[[Malayalam numerals|Malayalam]]
|lang15 symbol=൬
}}
'''6''' ('''six''') is the [[Natural number|natural number]] following [[5|5]] and preceding [[7|7]]. It is a [[Composite number|composite number]] and the smallest [[Perfect number|perfect number]].<ref name=":0" />

==In mathematics==
'''Six''' is the smallest positive integer which is neither a [[Square number|square number]] nor a [[Prime number|prime number]]. It is the second smallest [[Composite number|composite number]] after [[4|four]], equal to the [[Addition|sum]] and the [[Multiplication|product]] of its three proper [[Divisor|divisor]]s ({{num|1}}, {{num|2}} and {{num|3}}).<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=6|url=https://mathworld.wolfram.com/6.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref> As such, 6 is the only number that is both the sum and product of three consecutive positive numbers. It is the smallest [[Perfect number|perfect number]], which are numbers that are equal to their [[Aliquot sum|aliquot sum]], or sum of their proper divisors.<ref name=":0" /><ref>{{cite book |title=Number Story: From Counting to Cryptography |url=https://archive.org/details/numberstoryfromc00higg_612 |url-access=registration |last=Higgins |first=Peter |year=2008 |publisher=Copernicus |location=New York |isbn=978-1-84800-000-1 |page=[https://archive.org/details/numberstoryfromc00higg_612/page/n20 11] }}</ref> It is also the largest of the four [[Harshad number|all-Harshad number]]s (1, 2, [[4|4]], and 6).<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Harshad Number|url=https://mathworld.wolfram.com/HarshadNumber.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>

6 is a [[Pronic number|pronic number]] and the only semiprime to be.<ref>{{Cite web|url=https://oeis.org/A002378|title=Sloane's A002378: Pronic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2020-11-30}}</ref> It is the first discrete biprime (2 × 3)<ref>{{Cite OEIS|A001358 |Semiprimes (or biprimes): products of two primes. |access-date=2023-08-03 }}</ref> which makes it the first member of the (2 × ''q'') discrete biprime family, where ''q'' is a higher prime.  All primes above 3 are of the form 6''n'' ± 1 for ''n'' ≥ 1.

As a perfect number:
*6 is related to the [[Mersenne prime]] 3, since {{nowrap|2{{sup|1}}(2{{sup|2}} – 1) {{=}} 6}}. (The next perfect number is [[28 (number)|28]].)
*6 is the only even [[Perfect number|perfect number]] that is not the sum of successive odd cubes.<ref>David Wells, ''The Penguin Dictionary of Curious and Interesting Numbers''. London: Penguin Books (1987): 67</ref>
*6 is the root of the 6-aliquot tree, and is itself the [[Aliquot sum|aliquot sum]] of only one other number; the [[Square number|square number]], {{num|25}}.

Six is the first '''[[Unitary perfect number|unitary perfect number]]''', since it is the sum of its positive proper [[Unitary divisor|unitary divisor]]s, without including itself. Only five such numbers are known to exist; [[60 (number)|sixty]] (10 × 6) and [[90 (number)|ninety]] (15 × 6) are the next two.<ref>{{Cite OEIS|1=A002827|2=Unitary perfect numbers  |access-date=2016-06-01}}</ref>

It is the first ''primitive'' pseudoperfect number,<ref>{{Cite OEIS |A005835 |Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n. |access-date=2023-12-02 }}</ref> and all integers <math>n</math> that are multiples of 6 are pseudoperfect (all multiples of a pseudoperfect number are pseudoperfect); six is also the smallest [[Granville number]], or <math>\mathcal{S}</math>-perfect number.<ref name=OEIS>{{cite web |title=Granville number |url=http://oeis.org/ |work=OeisWiki |publisher=The Online Encyclopedia of Integer Sequences |access-date=27 March 2011 |archive-url=https://web.archive.org/web/20110329130407/http://oeis.org/ |archive-date=29 March 2011 |url-status=live}}</ref>

Unrelated to 6's being a perfect number, a [[Golomb ruler]] of length 6 is a "perfect ruler".<ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 72</ref> Six is a [[Congruent number|congruent number]].<ref>{{Cite OEIS|1=A003273|2=Congruent numbers  |access-date=2016-06-01}}</ref>

6 is the second [[Primary pseudoperfect number|primary pseudoperfect number]],<ref>{{Cite OEIS|1=A054377|2=Primary pseudoperfect numbers  |access-date=2018-11-02}}</ref> and [[Harmonic divisor number|harmonic divisor number]].<ref>{{Cite OEIS|1=A001599|2=Harmonic or Ore numbers  |access-date=2016-06-01}}</ref> It is also the second [[Superior highly composite number|superior highly composite number]],<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Superior Highly Composite Number|url=https://mathworld.wolfram.com/SuperiorHighlyCompositeNumber.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref> and the last to also be a [[Primorial|primorial]].

There are 6 non-equivalent ways in which [[100|100]] can be expressed as the sum of two prime numbers: (3 + 97), (11 + 89), (17 + 83), (29 + 71), (41 + 59) and (47 + 53).<ref>{{Cite OEIS|1=A065577|2=Number of Goldbach partitions of 10^n|access-date=2023-08-31}}</ref>

There is not a prime <math>p</math> such that the multiplicative order of 2 modulo <math>p</math> is 6, that is, <math>ord_p(2) = 6</math>
By [[Zsigmondy's theorem]], if <math>n</math> is a natural number that is not 1 or 6, then there is a prime <math>p</math> such that <math>ord_p(2) = n</math>. See {{OEIS link|A112927}} for such <math>p</math>.

The ring of integer of the sixth cyclotomic field {{math|'''Q'''(ζ<sub>6</sub>)}}, which is called [[Eisenstein integer]], has 6 units: ±1, ±ω, ±ω<sup>2</sup>, where <math>\omega = \frac{1}{2}(-1 + i\sqrt 3) = e^{2\pi i/3}</math>.

The [[Six exponentials theorem|six exponentials theorem]] guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Six Exponentials Theorem|url=https://mathworld.wolfram.com/SixExponentialsTheorem.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>

There are six basic [[Trigonometric functions|trigonometric functions]]: [[Sine and cosine|sin, cos]], sec, csc, tan, and cot.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Trigonometric Functions|url=https://mathworld.wolfram.com/TrigonometricFunctions.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>

The smallest non-[[Abelian group|abelian group]] is the [[Symmetric group|symmetric group]] <math>\mathrm {S_{3}}</math> which has [[Factorial|3!]] = 6 elements.<ref name=":0" />

Six is a [[Triangular number|triangular number]]<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Triangular Number|url=https://mathworld.wolfram.com/TriangularNumber.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref> and so is its square ({{num|36}}). It is the first octahedral number, preceding [[19 (number)|19]].<ref>{{Cite OEIS|1=A005900|2=Octahedral numbers  |access-date=2016-06-01}}</ref>

[[File:120px-Hexahedron-slowturn.gif|left|thumb|A regular [[Cube|cube]], with six [[Face (geometry)|faces]]]]

A six-sided [[Polygon|polygon]] is a [[Hexagon|hexagon]],<ref name=":0" /> one of the three [[Regular polygon|regular polygon]]s capable of [[Tessellation|tiling the plane]]. [[Figurate number]]s representing hexagons (including six) are called hexagonal numbers. Because 6 is the product of a power of 2 (namely 2<sup>1</sup>) with nothing but distinct Fermat primes (specifically 3), a regular hexagon is a [[Constructible polygon|constructible polygon]] with a [[Physics:Compass|compass]] and [[Straightedge|straightedge]] alone. A [[Hexagram|hexagram]] is a six-pointed geometric star figure (with the [[Schläfli symbol]] {6/2}, 2{3}, or <nowiki>{{3}}</nowiki>).

Six similar coins can be arranged around a central coin of the same radius so that each coin makes contact with the central one (and touches both its neighbors without a gap), but seven cannot be so arranged. This makes 6 the answer to the two-dimensional [[Kissing number problem|kissing number problem]].<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Kissing Number|url=https://mathworld.wolfram.com/KissingNumber.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref> The densest [[Sphere packing|sphere packing]] of the plane is obtained by extending this pattern to the [[Hexagon|hexagon]]al [[Lattice (group)|lattice]] in which each ''[[Circle|circle]]'' touches just six others.

There is only one non-trivial [[Magic hexagon|magic hexagon]]: it is of order-3 and made of nineteen cells, with a [[Magic constant|magic constant]] of 38. All rows and columns in a 6 × 6 [[Magic square|magic square]] collectively generate a [[Magic constant|magic sum]] of [[666 (number)|666]] (which is [[Doubly triangular number|doubly triangular]]). On the other hand, [[Graeco-Latin square]]s with order 6 do not exist; if <math>n</math> is a [[Natural number|natural number]] that is not [[2|2]] or 6, then there is a Graeco-Latin square of order <math>n</math>.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Euler's Graeco-Roman Squares Conjecture|url=https://mathworld.wolfram.com/EulersGraeco-RomanSquaresConjecture.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>

The [[Cube|cube]] is one of five [[Platonic solid]]s, with a total of six [[Square|square]]s as [[Face (geometry)|face]]s. It is the only regular polyhedron that can generate a [[Uniform honeycomb|uniform honeycomb]] on its own, which is also self-dual. The [[Cuboctahedron|cuboctahedron]], which is an [[Archimedean solid|Archimedean]] solid that is one of two [[Quasiregular polyhedron|quasiregular polyhedra]], has eight triangles and six squares as faces. Inside, its [[Vertex arrangement|vertex arrangement]] can be interpreted as three hexagons that intersect to form an equatorial hexagonal ''hemi-face'', by-which the cuboctahedron is dissected into [[Triangular cupola|triangular cupola]]s. This solid is also the only polyhedron with radial equilateral symmetry, where its edges and long radii are of equal length; its one of only four [[Polytope|polytope]]s with this property — the others are the hexagon, the [[Tesseract|tesseract]] (as the four-dimensional ''analogue'' of the cube), and the [[24-cell|24-cell]]. Only six polygons are [[Face (geometry)|faces]] of non-prismatic [[Uniform polyhedron|uniform polyhedra]] such as the Platonic solids or the Archimedean solids: the [[Triangle|triangle]], the [[Square|square]], the [[Pentagon|pentagon]], the hexagon, the [[Octagon|octagon]], and the [[Decagon|decagon]]. If self-dual images of the tetrahedron are considered distinct, then there are a total of six regular polyhedra that are formed by three different [[Weyl group]]s in the third dimension (based on [[Tetrahedral symmetry|tetrahedral]], [[Octahedral symmetry|octahedral]] and [[Icosahedral symmetry|icosahedral]] symmetries).

How closely the shape of an object resembles that of a perfect [[Sphere|sphere]] is called its '''[[Sphericity|sphericity]]''', calculated by:<ref>{{Cite journal |first=Hakon |last=Wadell |title=Volume, Shape, and Roundness of Quartz Particles |url=https://www.journals.uchicago.edu/doi/10.1086/624298 |journal=The Journal of Geology |volume=43 |issue=3 |year=1935 |pages=250–280 |doi=10.1086/624298 |bibcode=1935JG.....43..250W |jstor=30056250 |s2cid=129624905 }}</ref>

<math display="block"> \Psi = \frac{ \pi^{\frac{1}{3}} \left(6V_{p}\right)^{\frac{2}{3}} }{A_{p}} = \frac{A_s}{A_p},</math> where <math>A_s</math> is the [[Surface area|surface area]] of the sphere, <math>V_p</math> the volume of the object, and <math>A_p</math> the surface area of the object.

In [[Four-dimensional space|four dimensions]], there are a total of six convex regular polytopes: the [[5-cell|5-cell]], 8-cell, [[16-cell|16-cell]], [[24-cell|24-cell]], [[120-cell|120-cell]], and [[600-cell|600-cell]].

<math>\mathrm {S_{6}}</math>, with 720 = 6[[Factorial|!]] elements, is the only [[Finite group|finite]] symmetric group which has an outer automorphism. This automorphism allows us to construct a number of exceptional [[Philosophy:Mathematical object|mathematical object]]s such as the S(5,6,12) [[Steiner system]], the [[Projective plane|projective plane]] of order&nbsp;4, the four-dimensional [[5-cell|5-cell]], and the Hoffman-Singleton graph. A closely related result is the following theorem: 6 is the only natural number <math>n</math> for which there is a construction of <math>n</math> isomorphic objects on an <math>n</math>-[[Set theory|set]] <math>A</math>, invariant under all permutations of <math>A</math>, but not naturally in one-to-one correspondence with the elements of <math>A</math>. This can also be expressed [[Category theory|category theoretically]]: consider the [[Category (mathematics)|category]] whose objects are the <math>n</math> element sets and whose arrows are the [[Bijection|bijection]]s between the sets. This category has a non-trivial [[Functor|functor]] to itself only for <math>n = 6</math>.

In the [[Classification of finite simple groups|classification of finite simple groups]], twenty of twenty-six [[Sporadic group|sporadic group]]s in the [[Sporadic group#Organization|happy family]] are part of three families of groups which divide the order of the [[Monster group|friendly giant]], the largest sporadic group: five ''first generation'' [[Mathieu group]]s, seven ''second generation'' [[Subquotient|subquotient]]s of the [[Leech lattice]], and eight ''third generation'' [[Subgroup|subgroup]]s of the friendly giant. The remaining '''six''' sporadic groups do not divide the order of the friendly giant, which are termed the ''[[Pariah group|'''pariahs''']]'' ([[Lyons group|''Ly'']], [[O'Nan group|''O'N'']], [[Rudvalis group|''Ru'']], [[Janko group J4|''J''<sub>4</sub>]], [[Janko group J3|''J''<sub>3</sub>]], and [[Janko group J1|''J''<sub>1</sub>]]).<ref>{{Cite journal |last=Griess, Jr. |first=Robert L. |url=https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46608/222_2005_Article_BF01389186.pdf?sequence=1 |title=The Friendly Giant |journal=[[Inventiones Mathematicae]] |volume=69 |date=1982 |pages=91–96 |doi=10.1007/BF01389186 |bibcode=1982InMat..69....1G  |hdl=2027.42/46608 |mr=671653 |zbl=0498.20013 |s2cid=123597150 }}</ref>

===List of basic calculations===
{|class="wikitable" style="text-align: center; background: white"
|-
! style="width:105px;"|[[Multiplication]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!25
!50
!100
!1000
|-
|'''6 × ''x'''''
|'''6'''
|[[12 (number)|12]]
|[[18 (number)|18]]
|[[24 (number)|24]]
|[[30 (number)|30]]
|[[36 (number)|36]]
|[[42 (number)|42]]
|[[48 (number)|48]]
|[[54 (number)|54]]
|[[60 (number)|60]]
|[[66 (number)|66]]
|[[72 (number)|72]]
|[[78 (number)|78]]
|[[84 (number)|84]]
|[[90 (number)|90]]
|[[96 (number)|96]]
|[[102 (number)|102]]
|[[108 (number)|108]]
|[[114 (number)|114]]
|[[120 (number)|120]]
|[[150 (number)|150]]
|[[300 (number)|300]]
|[[600 (number)|600]]
|[[6000 (number)|6000]]
|}

{|class="wikitable" style="text-align: center; background: white"
|-
! style="width:105px;"|[[Division (mathematics)|Division]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
! style="width:5px;"|
!11
!12
!13
!14
!15
|-
|'''6 ÷ ''x'''''
|'''6'''
|3
|2
|1.5
|1.2
|1
|0.{{overline|857142}}
|0.75
|0.{{overline|6}}
|0.6
!
|0.{{overline|54}}
|0.5
|0.{{overline|461538}}
|0.{{overline|428571}}
|0.4
|-
|'''''x'' ÷ 6'''
|0.1{{overline|6}}
|0.{{overline|3}}
|0.5
|0.{{overline|6}}
|0.8{{overline|3}}
|1
|1.1{{overline|6}}
|1.{{overline|3}}
|1.5
|1.{{overline|6}}
!
|1.8{{overline|3}}
|2
|2.1{{overline|6}}
|2.{{overline|3}}
|2.5
|}

{|class="wikitable" style="text-align: center; background: white"
|-
! style="width:105px;"|[[Exponentiation]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
! style="width:5px;"|
!11
!12
!13
|-
|'''6{{sup|''x''}}'''
|'''6'''
|36
|[[216 (number)|216]]
|1296
|7776
|46656
|279936
|1679616
|10077696
|60466176
!
|362797056
|2176782336
|13060694016
|-
|'''''x''{{sup|6}}'''
|1
|[[64 (number)|64]]
|729
|4096
|15625
|46656
|117649
|262144
|531441
|1000000
!
|1771561
|2985984
|4826809
|}

==Greek and Latin word parts==

===''{{lang|grc-Latn|Hexa}}''===
'''''{{lang|grc-Latn|Hexa}}''''' is classical [[Social:Greek language|Greek]] for "six".<ref name=":0" /> Thus:
*"[[Hexadecimal]]" combines ''{{lang|grc-Latn|hexa-}}'' with the Latinate ''{{lang|la|decimal}}'' to name a number base of 16<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Hexadecimal|url=https://mathworld.wolfram.com/Hexadecimal.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
*A [[Hexagon|hexagon]] is a [[Regular polygon|regular polygon]] with six sides<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Hexagon|url=https://mathworld.wolfram.com/Hexagon.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
**''{{lang|fr|L'Hexagone}}'' is a French nickname for the continental part of [[Place:Metropolitan France|Metropolitan France]] for its resemblance to a [[Hexagon#Regular hexagon|regular hexagon]]
*A [[Hexahedron|hexahedron]] is a [[Polyhedron|polyhedron]] with six faces, with a cube being a special case<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Hexahedron|url=https://mathworld.wolfram.com/Hexahedron.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
*Hexameter is a poetic form consisting of six feet per line
*A "hex nut" is a [[Engineering:Nut (hardware)|nut]] with six sides, and a hex [[Engineering:Screw|bolt]] has a six-sided head
*The prefix "{{lang|grc-Latn|hexa-}}" also occurs in the systematic name of many [[Chemistry:Chemical compound|chemical compound]]s, such as [[Chemistry:Hexane|hexane]] which has 6 carbon atoms ({{chem2|C6H14}}).

===The prefix ''sex-''===
'''''Sex-''''' is a [[Social:Latin|Latin]] prefix meaning "six".<ref name=":0" /> Thus:
*''Senary'' is the ordinal adjective meaning "sixth"<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Base|url=https://mathworld.wolfram.com/Base.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
*People with sexdactyly have six fingers on each hand
*The measuring instrument called a [[Astronomy:Sextant|sextant]] got its name because its shape forms one-sixth of a whole [[Circle|circle]]
*A group of six musicians is called a sextet
*Six babies delivered in one birth are sextuplets
*[[Sexy prime]] pairs – Prime pairs differing by six are ''sexy'', because sex is the Latin word for six.<ref>{{cite book |last1=Chris K. Caldwell |last2=G. L. Honaker Jr. |date=2009 |title=Prime Curios!: The Dictionary of Prime Number Trivia |url=https://primes.utm.edu/curios/ |publisher=CreateSpace Independent Publishing Platform |page=11 |isbn=978-1-4486-5170-2 }}</ref><ref>{{Cite web|last=Weisstein|first=Eric W.|title=Sexy Primes|url=https://mathworld.wolfram.com/SexyPrimes.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>

The [[SI prefix]] for 1000<sup>6</sup> is [[Exa-|exa-]] (E), and for its reciprocal [[Atto-|atto-]] (a).

==Evolution of the Hindu-Arabic digit==
[[File:Edicts of Ashoka numerals.jpg|thumb|upright=1.5|The first appearance of 6 is in the Edicts of Ashoka {{Circa|250 BCE}}. These are [[Brahmi numerals|Brahmi numerals]], ancestors of Hindu-Arabic numerals.]]
[[File:Ashoka Brahmi numerals 256.jpg|thumb|right|upright=0.6|The first known digit "6" in the number "256" in Ashoka's Minor Rock Edict No.1 in Sasaram, {{Circa|250 BCE}}]]
The evolution of our modern digit 6 appears rather simple when compared with the other digits. The modern 6 can be traced back to the [[Brahmi numerals]] of {{wipe|India}}, which are first known from the Edicts of Ashoka {{Circa|250 BCE}}.<ref>{{cite book |last1=Hollingdale |first1=Stuart |title=Makers of Mathematics |date=2014 |publisher=Courier Corporation |isbn=978-0-486-17450-1 |pages=95–96 |url=https://books.google.com/books?id=ZET_AwAAQBAJ&pg=PA95 |language=en}}</ref><ref>{{cite book |last1=Publishing |first1=Britannica Educational |title=The Britannica Guide to Theories and Ideas That Changed the Modern World |date=2009 |publisher=Britannica Educational Publishing |isbn=978-1-61530-063-1 |page=64 |url=https://books.google.com/books?id=QcOcAAAAQBAJ&pg=PA65 |language=en}}</ref><ref>{{cite book |last1=Katz |first1=Victor J. |last2=Parshall |first2=Karen Hunger |title=Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century |date=2014 |publisher=Princeton University Press |isbn=978-1-4008-5052-5 |page=105 |url=https://books.google.com/books?id=nQLHAgAAQBAJ&pg=PA105 |language=en}}</ref><ref>{{cite book |last1=Pillis |first1=John de |title=777 Mathematical Conversation Starters |date=2002 |publisher=MAA |isbn=978-0-88385-540-9 |page=286 |url=https://books.google.com/books?id=YB4wS-N9qb0C&pg=PA286 |language=en}}</ref> It was written in one stroke like a cursive lowercase e rotated 90 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.<ref>Georges Ifrah, ''The Universal History of Numbers: From Prehistory to the Invention of the Computer'' transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.66</ref>

On the [[Engineering:Seven-segment display|seven-segment display]]s of calculators and watches, 6 is usually written with six segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on; for calculators that can display results in hexadecimal, a 6 that looks like a "b" is not practical.

Just as in most modern [[Typeface|typeface]]s, in typefaces with [[Text figures|text figures]] the character for the digit 6 usually has an ascender, as, for example, in [[File:Text figures 036.svg|52px]].<ref>{{Cite book|last=Negru|first=John|url=https://books.google.com/books?id=4A9UAAAAMAAJ&q=text+figures+the+6+character+usually+has+an+ascender,|title=Computer Typesetting|date=1988|publisher=Van Nostrand Reinhold|isbn=978-0-442-26696-7|page=59|language=en|quote=slight ascenders that rise above the cap height ( in 4 and 6 )}}</ref>

This digit resembles an inverted ''9''. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.

==In music==
[[File:Guitar 1.jpg|thumb|150px|A standard guitar has six strings.]]

===In artists===
*''{{lang|fr|Les Six}}'' ("The Six" in English) was a group consisting of the French composers {{lang|fr|Georges Auric|italic=no}}, {{lang|fr|Louis Durey|italic=no}}, {{lang|fr|Arthur Honegger|italic=no}}, {{lang|fr|Darius Milhaud|italic=no}}, {{lang|fr|Francis Poulenc|italic=no}} and {{lang|fr|Germaine Tailleferre|italic=no}} in the 1920s<ref>{{Cite book|last1=Auric|first1=Georges|url=https://books.google.com/books?id=gkkWBAAAQBAJ&q=Les+Six&pg=PR6|title=Caramel Mou and Other Great Piano Works of "Les Six": Pieces by Auric, Durey, Honegger, Milhaud, Poulenc and Tailleferre|last2=Durey|first2=Louis|last3=Honegger|first3=Arthur|last4=Milhaud|first4=Darius|last5=Poulenc|first5=Francis|last6=Tailleferre|first6=Germaine|date=2014-08-20|publisher=Courier Corporation|isbn=978-0-486-49340-4|language=fr}}</ref>
* Bands with the number six in their name include Six Organs of Admittance,<ref>{{Cite web|title=Six Organs of Admittance|url=http://www.sixorgans.com/|access-date=2020-08-03|website=www.sixorgans.com}}</ref> 6 O'Clock Saints, Electric Six,<ref>{{Cite web|title=Electric Six {{!}} Biography, Albums, Streaming Links|url=https://www.allmusic.com/artist/electric-six-mn0000163059|access-date=2020-08-03|website=AllMusic|language=en-us}}</ref> Eve 6, Los Xey (''{{lang|eu|sei}}'' is Basque for "six"), Out On Blue Six, Six In Six, Sixpence None the Richer,<ref>{{Cite web|date=2020-05-19|title=Sixpence None The Richer|url=https://www.grammy.com/grammys/artists/sixpence-none-richer/14788|access-date=2020-08-04|website=GRAMMY.com|language=en}}</ref> Slant 6,<ref>{{Cite web|title=Slant 6 {{!}} Biography & History|url=https://www.allmusic.com/artist/slant-6-mn0000749444/biography|access-date=2020-08-04|website=AllMusic|language=en-us}}</ref> Vanity 6, and You Me At Six<ref>{{Cite web|title=You Me at Six {{!}} Biography & History|url=https://www.allmusic.com/artist/you-me-at-six-mn0001982318/biography|access-date=2020-08-04|website=AllMusic|language=en-us}}</ref>
* #6 is the pseudonym of {{wipe|United States}} musician Shawn Crahan, when performing with the band Slipknot

===In instruments===
*A standard [[Engineering:Guitar|guitar]] has six strings<ref>{{Cite web|title=Definition of GUITAR|url=https://www.merriam-webster.com/dictionary/guitar|access-date=2020-08-04|website=www.merriam-webster.com|language=en}}</ref>
*Most woodwind instruments have six basic holes or keys (e.g., bassoon, clarinet, pennywhistle, saxophone); these holes or keys are usually not given numbers or letters in the fingering charts

===In music theory===
*There are six whole tones in an octave.<ref>{{Cite book|last=D'Amante|first=Elvo|url=https://books.google.com/books?id=_uBIm5QyxbsC&q=six+whole+tones+in+an+octave.&pg=PA194|title=Music Fundamentals: Pitch Structures and Rhythmic Design|date=1994-01-01|publisher=Scarecrow Press|isbn=978-1-4616-6985-2|page=194|language=en|quote=The division of an octave into six equal parts is referred to as the whole-tone scale}}</ref>
*There are six semitones in a tritone.<ref>{{Cite book|last=Horsley|first=Charles Edward|url=https://books.google.com/books?id=kDIDAAAAQAAJ&q=six+semitones+in+a+tritone.&pg=PA4|title=A Text Book of Harmony: For the Use of Schools and Students|date=1876|publisher=Sampson Low, Marston, Searle, & Rivington|page=4|language=en|quote=Like the Tritone, it contains six semitones}}</ref>

===In works===
*"Six geese a-laying" were given as a present on the sixth day in the popular Christmas carol, "The Twelve Days of Christmas".<ref>{{Cite book|last=Tribble|first=Mimi|url=https://books.google.com/books?id=rv0G4iotU24C&q=Six+geese+a-laying&pg=PA143|title=300 Ways to Make the Best Christmas Ever!: Decorations, Carols, Crafts & Recipes for Every Kind of Christmas Tradition|date=2004|publisher=Sterling Publishing Company, Inc.|isbn=978-1-4027-1685-0|page=145|language=en|quote=Six geese a-laying}}</ref>
*Divided in six arias, ''Hexachordum Apollinis'' is generally regarded as one of the pinnacles of Johann Pachelbel's oeuvre.<ref>{{Cite book|last=Staines|first=Joe|url=https://books.google.com/books?id=g1ga2hNiiAgC&q=six+arias,+Hexachordum+Apollinis&pg=PA393|title=The Rough Guide to Classical Music|date=2010-05-17|publisher=Penguin|isbn=978-1-4053-8321-9|page=393|language=en|quote=...the six arias with variations collected under the title Hexachordum Apollinis (1699)...}}</ref>
*The theme of the sixth album by Dream Theater, ''Six Degrees of Inner Turbulence'', was the number six: the album has six songs, and the sixth song—that is, the complete second disc—explores the stories of six individuals suffering from various mental illnesses.<ref>{{Cite book|last1=Hegarty|first1=Paul|url=https://books.google.com/books?id=fsaoAwAAQBAJ&q=Six+Degrees+Of+Inner+Turbulence&pg=PT140|title=Beyond and Before: Progressive Rock since the 1960s|last2=Halliwell|first2=Martin|date=2011-06-23|publisher=Bloomsbury Publishing USA|isbn=978-1-4411-1480-8|page=169|language=en|quote=Six Degrees of Inner Turbulence}}</ref>
*[[Biography:Aristotle|Aristotle]] gave six elements of tragedy, the first of which is Mythos.<ref>{{Cite book|last=Curran|first=Angela|url=https://books.google.com/books?id=7wOpCgAAQBAJ&q=Aristotle+gave+six+elements+of+tragedy,&pg=PA133|title=Routledge Philosophy Guidebook to Aristotle and the Poetics|date=2015-10-05|publisher=Routledge|isbn=978-1-317-67706-2|page=133|language=en|quote=THE SIX QUALITATIVE ELEMENTS OF TRAGEDY}}</ref>

==In religion==
[[File:Star of David (bold).svg|50px|right]]
{{See also|666 (number){{!}}666}}

===Judaism===
*Six points on a [[Star of David]]<ref>{{Cite book|last=Plaut|first=W. Gunther|url=https://books.google.com/books?id=U18RAQAAIAAJ|title=The Magen David: How the Six-pointed Star Became an Emblem for the Jewish People|date=1991|publisher=B'nai B'rith Books|isbn=978-0-910250-16-0|language=en|quote=How the Six-pointed Star Became an Emblem for the Jewish People}}</ref>
*Six orders of the [[Religion:Mishnah|Mishnah]]<ref>{{Cite book|last=Lauterbach|first=Jacob Zallel|url=https://books.google.com/books?id=UV0MAQAAIAAJ&q=Six+orders+of+the+Mishnah&pg=PA9|title=Midrash and Mishnah: A Study in the Early History of the Halakah|date=1916|publisher=Bloch|page=9|language=en|quote=Six orders of Mishnah}}</ref>
*Six symbolic foods placed on the Passover Seder Plate<ref>{{Cite book|last1=Rosen|first1=Ceil|url=https://books.google.com/books?id=Uq2DIIWPyVUC&q=Six+symbolic+foods+placed+on+the+Passover+Seder+Plate&pg=PA79|title=Christ in the Passover|last2=Rosen|first2=Moishe|date=2006-05-01|publisher=Moody Publishers|isbn=978-1-57567-480-3|page=79|language=en|quote=Six symbolic foods}}</ref>
*[[Religion:God|God]] took six days to create the world in the [[Religion:Old Testament|Old Testament]] [[Religion:Book of Genesis|Book of Genesis]];<ref>{{Cite book|last=Repcheck|first=Jack|url=https://books.google.com/books?id=sxwcncChs-YC&q=God+took+six+days+to+create+the+world+in+the+Old+Testament+Book+of+Genesis;&pg=PT26|title=The Man Who Found Time: James Hutton And The Discovery Of Earth's Antiquity|date=2008-12-15|publisher=Basic Books|isbn=978-0-7867-4399-5|language=en|quote=it actually took only six days to create the earth}}</ref> humankind was created on day 6. In the ''City of God'', [[Biography:Augustine of Hippo|Augustine of Hippo]] suggested (book 11, chapter 30) that God's creation of the world took six days because 6 is a [[Perfect number|perfect number]].<ref>{{Cite web|title=CHURCH FATHERS: City of God, Book XI (St. Augustine)|url=https://www.newadvent.org/fathers/120111.htm|access-date=2020-08-04|website=www.newadvent.org|quote=These works are recorded to have been completed in six days (the same day being six times repeated), because six is a perfect number}}</ref>
*The [[Religion:Judaism|Jewish]] holiday of Shavuot starts on the sixth day of the [[History:Hebrew calendar|Hebrew]] month of Sivan<ref>{{Cite book|last1=Grossman|first1=Grace Cohen|url=https://books.google.com/books?id=9kj0AAAAMAAJ&q=Jewish+holiday+of+Shavuot+starts+on+the+sixth+day+of+the+Hebrew+month+of+Sivan|title=Judaica at the Smithsonian: Cultural Politics as Cultural Model|last2=Ahlborn|first2=Richard E.|last3=Institution|first3=Smithsonian|date=1997|publisher=Smithsonian Institution Press|page=228|language=en|quote=Shavuot falls on the sixth day of the Hebrew month of Sivan}}</ref>
*[[Unsolved:Seraph|Seraph]]s have six wings.<ref>{{Cite book|last=Robertson|first=William Archibald Scott|url=https://books.google.com/books?id=BRYHAAAAQAAJ&q=Seraphs+have+six+wings.&pg=PA91|title=The crypt of Canterbury cathedral; its architecture, its history, and its frescoes|date=1880|publisher=Mitchell & Hughes|page=91|language=en|quote=...but seraphs, with six wings}}</ref>

===Islam===
*There are [[Religion:Iman (Islam)|Six articles of faith]]<ref>{{Cite book|last=Shapera|first=Paul M.|url=https://books.google.com/books?id=ge9Kc_VlCxoC&q=Six+articles+of+belief&pg=PA10|title=Iran's Religious Leaders|date=2009-08-15|publisher=The Rosen Publishing Group, Inc|isbn=978-1-4358-5283-9|page=10|language=en|quote=Islam has six articles of faith}}</ref>
*Six points on a [[Religion:Seal of Solomon|Seal of Solomon]]
*Fasting six days of [[Religion:Shawwal|Shawwal]], together with the month of [[Religion:Ramadan|Ramadan]], is equivalent to fasting the whole year<ref>{{Cite book|last=Algül|first=Hüseyin|url=https://books.google.com/books?id=mk-E3rDUFgIC&q=six+days+of+Shawwal,&pg=PA65|title=The Blessed Days and Nights of the Islamic Year|date=2005|publisher=Tughra Books|isbn=978-1-932099-93-5|page=65|language=en|quote=...it was blessed to fast for six days in the month of Shawwal...}}</ref>
*The heavens and earth were created in six days according to the [[Religion:Quran|Quran]]:<ref>{{Cite web |title=Surah Qaf - 38 |url=https://quran.com/qaf/38 |access-date=2023-08-28 |website=Quran.com |language=en}}</ref>
{{blockquote|Indeed, We created the heavens and the earth and everything in between in six Days,<sup>1</sup> and We were not ˹even˺ touched with fatigue.<sup>2</sup>|[[Religion:Surah|Surah]] Qaf:38}}
Note 1: The word day is not always used in the Quran to mean a 24-hour period. According to Surah Al-Hajj (The Pilgrimage):47, a heavenly Day is 1000 years of our time. The [[Religion:Last Judgment|Day of Judgment]] will be 50,000 years of our time - Surah Al-Maarij (The Ascending Stairways):4. Hence, the six Days of creation refer to six eons of time, known only by Allah.

Note 2: Some [[Religion:Ulama|Islamic scholars]] believe this verse comes in response to Exodus 31:17, which says, "The Lord made the heavens and the earth in six days, but on the seventh day He rested and was refreshed."

===Others===
*In [[Philosophy:Āstika and nāstika|Hindu theology]], a ''trasarenu'' is the combination of six celestial {{Lang|sa|paramānus}} ([[Philosophy:Vaisheshika#The atomic theory|atoms]]).
*In Taoism:
**Six Lines of a [[Philosophy:I Ching|Hexagram]]
**Six Ministries of Huang Di<ref>{{Cite book|last1=Bary|first1=William Theodore De|url=https://books.google.com/books?id=OeaKKrD6z70C&q=Six+Ministries+of+Huang+Di&pg=PA12|title=Sources of Chinese Tradition|last2=DeBary|first2=William T.|last3=Chan|first3=Wing-tsit|last4=Lufrano|first4=Richard|last5=Ching|first5=Julia|last6=Johnson|first6=David|last7=Liu|first7=Kwang-Ching|last8=Mungello|first8=David|date=1999|publisher=Columbia University Press|isbn=978-0-231-11270-3|language=en|quote=...and the Six Ministries were made...}}</ref>

==In science==
===Astronomy===
*[[Astronomy:Messier object|Messier object]] M6, a magnitude 4.5 [[Astronomy:Open cluster|open cluster]] in the constellation [[Astronomy:Scorpius|Scorpius]], also known as the [[Astronomy:Butterfly Cluster|Butterfly Cluster]]<ref>{{Cite book|last=Rhoads|first=Samuel E.|url=https://books.google.com/books?id=3ISFAAAAMAAJ&q=Messier+object+M6|title=The Sky Tonight: A Guided Tour of the Stars Over Hawaiʻi|date=1996|publisher=Bishop Museum Press|isbn=978-0-930897-93-2|language=en|quote=Three Messier objects are visible in this part of the sky : M6, M7 and M8 .}}</ref>
*The [[Astronomy:New General Catalogue|New General Catalogue]] object [[Astronomy:NGC 6|NGC 6]], a [[Spiral galaxy|spiral galaxy]] in the [[Astronomy:Constellation|constellation]] Andromeda
*The Roman numeral VI:
**Stands for [[Astronomy:Subdwarf|subdwarf]]s in the [[Astronomy:Stellar classification|Yerkes spectral classification scheme]]
**(Usually) stands for the sixth-discovered satellite of a planet or minor planet (e.g. Jupiter VI)
*[[Astronomy:6 Hebe|6 Hebe]]

===Biology===
[[File:Bienenwabe mit Eiern und Brut 5.jpg|thumb|150px|The cells of a beehive are six-sided.]]
*The cells of a beehive are [[Hexagon|six-sided]].<ref>{{Cite book|last=Sedgwick|first=Marcus|url=https://books.google.com/books?id=3xpSlkslWsQC&q=The+cells+of+honeycomb+are+six-sided&pg=PA145|title=White Crow|date=2011-07-05|publisher=Roaring Brook Press|isbn=978-1-4299-7634-3|page=145|language=en|quote=The cells of honeycombs are six-sided because a hexagon is the most material-efficient tessellation}}</ref>
*Insects have six [[Biology:Leg|leg]]s (see [[Biology:Hexapoda|Hexapoda]]).<ref>{{Cite book|last=Parker|first=Steve|url=https://books.google.com/books?id=XpHiTv2WvakC&q=Insects+have+six+legs.&pg=PA16|title=Ant Lions, Wasps & Other Insects|date=2005|publisher=Capstone|isbn=978-0-7565-1250-7|page=16|language=en|quote=Insects have six legs each...}}</ref>
*Six kingdoms in the [[Biology:Taxonomic rank|taxonomic rank]] below domain (biology); Animalia, Plantae, [[Biology:Fungi|Fungi]], Protista, [[Biology:Archaea|Archaea]]/Archaeabacteria, and [[Biology:Bacteria|Bacteria]]/Eubacteria. See [[Biology:Kingdom|Kingdom]].<ref>{{Cite book|last1=Pendarvis|first1=Murray P.|url=https://books.google.com/books?id=45OFDwAAQBAJ&q=Six+kingdoms+in+the+taxonomic+rank+below+domain+(biology);&pg=PA205|title=Exploring Biology in the Laboratory: Core Concepts|last2=Crawley|first2=John L.|date=2019-02-01|publisher=Morton Publishing Company|isbn=978-1-61731-899-3|page=10|language=en|quote=...presently at least six kingdoms are recognized;}}</ref>
*The six elements most common in biomolecules are called the CHNOPS elements; the letters stand for the chemical abbreviations of [[Chemistry:Carbon|carbon]], [[Chemistry:Hydrogen|hydrogen]], [[Chemistry:Nitrogen|nitrogen]], [[Chemistry:Oxygen|oxygen]], [[Chemistry:Phosphorus|phosphorus]], and [[Chemistry:Sulfur|sulfur]]. See [[Astronomy:CHON|CHON]].<ref>{{Cite book|last=Mader|first=Sylvia S.|url=https://books.google.com/books?id=IS3cMTwyOfIC&q=six+elements+most+common+in+biomolecules+are+called+the+CHNOPS|title=Biology|date=2004|publisher=McGraw-Hill|isbn=978-0-07-291934-9|page=20|language=en|quote=The acronym CHNOPS helps us remember these six elements}}</ref>

===Chemistry===
[[File:Benzene structure.png|200px|right|A [[Physics:Molecule|molecule]] of benzene has a ring of six carbon and six hydrogen atoms.]]
*A benzene molecule has a ring of six carbon atoms.<ref>{{Cite book|last=Dufour |first=Fritz |url=https://books.google.com/books?id=nwBvDwAAQBAJ&q=benzene+molecule+has+a+ring+of+six+carbon+atoms.&pg=PA100|title=The Realities of Reality - Part II: Making Sense of Why Modern Science Advances |volume=1 |date=2018-09-19|publisher=Fritz Dufour|page=100|language=en|quote=The benzene molecule has its six carbon atoms in a ring}}{{self-published inline|date=November 2023}}</ref>
*6 is the [[Physics:Atomic number|atomic number]] of carbon.<ref>{{Cite book|last1=Starr|first1=Cecie|url=https://books.google.com/books?id=uxbTCQAAQBAJ&q=6+is+the+atomic+number+of+carbon.&pg=PT46|title=Biology Today and Tomorrow without Physiology|last2=Evers|first2=Christine|date=2012-05-10|publisher=Cengage Learning|isbn=978-1-133-36536-5|page=25|language=en|quote=For example, the atomic number of carbon is 6,}}</ref>
*The sixfold [[Symmetry|symmetry]] of snowflakes arises from the [[Hexagon|hexagon]]al [[Chemistry:Crystal structure|crystal structure]] of [[Earth:Ice|ordinary ice]].<ref>{{Cite book|last1=Webb|first1=Stephen|url=https://books.google.com/books?id=3AJdTYu3m5sC&q=sixfold+symmetry+of+snowflakes+arises+from+the+hexagonal+crystal&pg=PA16|title=Out of this World: Colliding Universes, Branes, Strings, and Other Wild Ideas of Modern Physics|last2=Webb|first2=Professor of Australian Studies Stephen|date=2004-05-25|publisher=Springer Science & Business Media|isbn=978-0-387-02930-6|page=16|language=en|quote=snowflake, with its familiar sixfold rotational symmetry}}</ref>
*A hexamer is an oligomer made of six subunits.

===Medicine===
*There are six tastes in traditional Indian medicine ([[Philosophy:Ayurveda|Ayurveda]]): sweet, sour, salty, bitter, pungent, and astringent. These tastes are used to suggest a diet based on the symptoms of the body.<ref>{{Cite book|last1=Woo|first1=Teri Moser|url=https://books.google.com/books?id=2Q5hCgAAQBAJ&q=six+tastes+in+traditional+Indian+Medicine+called+Ayurveda:+sweet,+sour,+salty,+bitter,+pungent,+and+astringent.&pg=PA145|title=Pharmacotherapeutics For Advanced Practice Nurse Prescribers|last2=Robinson|first2=Marylou V.|date=2015-08-03|publisher=F.A. Davis|isbn=978-0-8036-4581-3|page=145|language=en|quote=Ayurvedic herbology is based on the tridoshic theory that there exist six basic tastes}}</ref>
*Phase 6 is one of six pandemic influenza phases.<ref>{{Cite book|url=https://books.google.com/books?id=ExkKjZre1f8C&q=Phase+6+is+one+of+six+pandemic+influenza+phases.&pg=PA8|title=Pandemic Influenza Preparedness and Response Guidance for Healthcare Workers and Healthcare Employers|date=2007|publisher=OSHA, U.S. Department of Labor|page=8|language=en|quote=The WHO Plan describes six phases of increasing public health risk associated with the emergence of a new influenza}}</ref>

===Physics===
[[File:Standard Model of Elementary Particles.svg|thumb|right|200px|In the [[Physics:Standard Model|Standard Model]] of particle physics, there are six types of quarks and six types of leptons.]]
*In the Standard Model of particle physics, there are six types of quarks and six types of [[Physics:Leptons|leptons]].<ref>{{Cite book|last=Sanghera|first=Paul|url=https://books.google.com/books?id=FaZzqwzD1E4C&q=there+are+six+types+of+quarks+and+six+types+of+leptons.&pg=PA64|title=Quantum Physics for Scientists and Technologists: Fundamental Principles and Applications for Biologists, Chemists, Computer Scientists, and Nanotechnologists|date=2011-03-08|publisher=John Wiley & Sons|isbn=978-0-470-92269-9|page=64|language=en|quote=...there are six types of quarks and six types of leptons.}}</ref>
*In [[Physics:Statistical mechanics|statistical mechanics]], the [[Physics:Ice-type model|six-vertex model]] has six possible configurations of arrows at each vertex<ref>{{Cite book|last1=Jimbo|first1=M.|url=https://books.google.com/books?id=RLErAAAAYAAJ&q=tn+statistical+mechanics,+the+six-vertex+model|title=Integrable Systems in Quantum Field Theory and Statistical Mechanics|last2=Jimbo|first2=Michio|last3=Miwa|first3=Tetsuji|last4=Tsuchiya|first4=Akihiro|date=1989|publisher=Academic Press|isbn=978-0-12-385342-4|page=588|language=en|quote=Allowed configurations in the six-vertex model and their statistical weights}}</ref>
*There are six colors in the RGB color wheel: (primary) red, blue, green, (secondary) cyan, magenta, and yellow. (See Tertiary color)<ref>{{Cite book|last=Sloan|first=Robin James Stuart|url=https://books.google.com/books?id=rI_YCQAAQBAJ&q=six+colors+in+the+RGB+color+wheel:+(primary)+red,+blue,+green,+(secondary)+cyan,+magenta,+and+yellow.&pg=PA34|title=Virtual Character Design for Games and Interactive Media|date=2015-05-07|publisher=CRC Press|isbn=978-1-4665-9820-1|page=34|language=en|quote=placing six primaries around the wheel in the following order: red, yellow, green, cyan, blue, magenta.}}</ref>
*In [[Three-dimensional space|three-dimensional]] [[Euclidean space]], there are six unknown [[Physics:Reaction|support reactions]] for a [[Statically indeterminate|statically determinate]] structure: one [[Physics:Force|force]] in each of the three dimensions, and one [[Physics:Moment|moment]] through each of three possible orthogonal [[Plane (geometry)|plane]]s.

==In sports==
* The Original Six teams in the National Hockey League are Toronto, Chicago, Montreal, New York, Boston, and Detroit.<ref>{{Cite book|last=Bamford|first=Tab|url=https://books.google.com/books?id=LjopDQAAQBAJ&q=Original+Six+teams+in+the+National+Hockey+League&pg=PT61|title=100 Things Blackhawks Fans Should Know & Do Before They Die|date=2016-10-15|publisher=Triumph Books|isbn=978-1-63319-638-4|language=en|quote=the Original Six}}</ref> They are the oldest remaining teams in the league, though not necessarily the first six; they comprised the entire league from 1942 to 1967.
* Number of players:
** In association football (soccer), the number of substitutes combined by both teams, that are allowed in the game.
** In box lacrosse, the number of players per team, including the goaltender, that are on the floor at any one time, excluding penalty situations.<ref>{{Cite book|last=Stillwell|first=Jim L.|url=https://books.google.com/books?id=5k5LAAAAYAAJ&q=box+lacrosse,+the+number+of+players+per+team,+including+the+goaltender,+that+are+on+the+floor+at+any+one+time,|title=Making and Using Creative Play Equipment|date=1987|publisher=Human Kinetics Publishers|isbn=978-0-87322-084-2|page=36|language=en|quote=Indoor Lacrosse . This is played with six players per team}}</ref>
** In ice hockey, the number of players per team, including the goaltender, that are on the ice at any one time during regulation play, excluding penalty situations. (Some leagues reduce the number of players on the ice during overtime.)<ref>{{Cite book|last=Williams|first=Heather|url=https://books.google.com/books?id=6NSaDwAAQBAJ&q=ice+hockey,+the+number+of+players+per+team,+including+the+goaltender,+that+are+on+the+ice&pg=PA16|title=Hockey: A Guide for Players and Fans|date=2019|publisher=Capstone|isbn=978-1-5435-7458-6|page=16|language=en|quote=There are six players per team on the ice at one time.}}</ref>
** In volleyball:
*** Six players from each team on each side play against each other.<ref>{{Cite book|last=Sports|first=The National Alliance For Youth|url=https://books.google.com/books?id=OTGWAAAAQBAJ&q=volleyball:+Six+players+from+each+team+on+each+side+play+against+each+other.&pg=PA48|title=Coaching Volleyball For Dummies|date=2009-05-11|publisher=John Wiley & Sons|isbn=978-0-470-53398-7|page=48|language=en|quote=In a regulation volleyball match with six players on each side of the court,}}</ref>
*** Standard rules only allow six total substitutions per team per set. (Substitutions involving the libero, a defensive specialist who can only play in the back row, are not counted against this limit.)
** Six-man football is a variant of American or Canadian football, played by smaller schools with insufficient enrollment to field the traditional 11-man (American) or 12-man (Canadian) squad.<ref>{{Cite web|title=sixmanfootball.com|url=http://www.sixmanfootball.com/|access-date=2020-08-06|website=www.sixmanfootball.com}}</ref>
* Scoring:
** In both American and Canadian football, 6 points are awarded for a touchdown.<ref>{{Cite web|title=How Football Teams Can Score Points in Game Play|url=https://www.dummies.com/sports/football/how-football-teams-can-score-points-in-game-play/|access-date=2020-08-06|website=dummies|language=en}}</ref>
** In Australian rules football, six points are awarded for a goal, scored when a kicked ball passes between the defending team's two inner goalposts without having been touched by another player.
** In cricket, six runs are scored for the batting team when the ball is hit to the boundary or the ground beyond it without having touched the ground in the field.
* In basketball, the [[Engineering:Basketball (ball)|ball]] used for women's full-court competitions is designated "size 6".<ref>{{Cite web|date=2018-09-12|title=Basketball Sizes Chart: What Size Ball Should a Player Use?|url=https://www.basketballforcoaches.com/basketball-sizes/|access-date=2020-08-06|website=Basketball For Coaches|language=en-US}}</ref>
* In pool and snooker one its table contains six pockets.
* In most rugby league competitions (but not the Super League, which uses static squad numbering), the jersey number 6 is worn by the starting {{rlp|fe}} (Southern Hemisphere term) or {{rlp|so}} (Northern Hemisphere term).
* In rugby union, the starting blindside flanker wears jersey number 6. (Some teams use "left" and "right" flankers instead of "openside" and "blindside", with 6 being worn by the starting left flanker.)<ref>{{Cite web|date=2019-02-01|title=Rugby flanker (#6 & #7): A position specific guide|url=https://atroxrugby.com/rugby-flanker/|access-date=2020-08-06|website=Atrox Rugby|language=en-US}}</ref>

==In technology==
[[File:U+2678 DejaVu Sans.svg|50px|right|6 as a resin identification code, used in recycling.]]
*On most phones, the 6 key is associated with the letters M, N, and O, but on the [[Engineering:BlackBerry Pearl|BlackBerry Pearl]] it is the key for J and K, and on the BlackBerry 8700 series and Curve 8900 with full keyboard, it is the key for F
*The "6-meter band" in amateur radio includes the frequencies from 50 to 54&nbsp;MHz
*6 is the [[Resin identification code|resin identification code]] used in recycling to identify [[Chemistry:Polystyrene|polystyrene]]<ref>{{Cite book|last=Stevens|first=E. S.|url=https://books.google.com/books?id=AFO9Cajtv6EC&q=6+is+the+resin+identification+code+used+in+recycling+to+identify+polystyrene&pg=PA44|title=Green Plastics: An Introduction to the New Science of Biodegradable Plastics|date=2002|publisher=Princeton University Press|isbn=978-0-691-04967-0|page=45|language=en}}</ref>

==In calendars==
*In the ancient Roman calendar, Sextilis was the sixth month. After the [[Julian calendar|Julian reform]], June became the sixth month and Sextilis was renamed August<ref>{{Cite book|last=Bunson|first=Matthew|url=https://books.google.com/books?id=T5tic2VunRoC&q=Roman+calendar,+Sextilis+was+the+sixth+month&pg=PA90|title=Encyclopedia of the Roman Empire|date=2014-05-14|publisher=Infobase Publishing|isbn=978-1-4381-1027-1|page=90|language=en|quote=Augustus was also originally called Sextilis, the sixth month.}}</ref>
*Sextidi was the sixth day of the ''décade'' in the French Revolutionary calendar<ref>{{Cite book|last=Nicolas|first=Sir Nicholas Harris|url=https://books.google.com/books?id=VFQuAAAAYAAJ&q=Sextidi+was+the+sixth+day+of+the+decade+in+the+French+Revolutionary+calendar&pg=PA172|title=The Chronology of History: Containing Tables, Calculations and Statements, Indispensable for Ascertaining the Dates of Historical Events and of Public and Private Documents from the Earliest Period to the Present Time|date=1833|publisher=Longham, Rees, Orme, Brown, Green, & Longman and John Taylor|page=172|language=en|quote=SEXTIDI, or " Jour de la Révolution, "}}</ref>

==In the arts and entertainment==
===Games===
*The number of sides on a cube, hence the highest number on a standard die<ref>{{Cite book|last=Schumer|first=Peter D.|url=https://books.google.com/books?id=tV__OQ8LZcgC&q=highest+number+on+a+standard+six+sided++die&pg=PA88|title=Mathematical Journeys|date=2004-02-11|publisher=John Wiley & Sons|isbn=978-0-471-22066-4|page=88|language=en|quote=Roll two dice, a standard six-sided die numbered 1 through 6}}</ref>
*The six-sided tiles on a hex grid are used in many tabletop and board games.
*The highest number on one end of a standard domino

===Comics and cartoons===
*''The Super 6'', a 1966 animated cartoon series featuring six different super-powered heroes.<ref>{{Cite web|last=DataBase|first=The Big Cartoon|title=The Super 6 Episode Guide -DePatie-Freleng Ent|url=https://www.bcdb.com/cartoons/Other_Studios/D/DePatie-Freleng_Enterprises/The_Super_6/index.html|archive-url=https://archive.today/20130425025523/http://www.bcdb.com/cartoons/Other_Studios/D/DePatie-Freleng_Enterprises/The_Super_6/index.html|url-status=dead|archive-date=April 25, 2013|access-date=2020-08-06|website=Big Cartoon DataBase (BCDB)|language=en-US}}</ref>

===Literature===
*''The Power of Six'' is a book written by Pittacus Lore, and the second in the Lorien Legacies series.<ref>{{Cite web|title='The Power of Six' trailer|url=https://ew.com/article/2011/08/02/the-power-of-six-trailer/|access-date=2020-08-06|website=EW.com|language=EN}}</ref>
*Number 6 is a character in the book series Lorien Legacies.

===TV===
* Number Six (Tricia Helfer) is a family of fictional characters from the reimagined science fiction television series, ''Battlestar Galactica.''
*Number 6, the main protagonist in ''The Prisoner'' played by Patrick McGoohan, and portrayed by Jim Caviezel in the remake.
*Six is a character in the television series ''Blossom'' played by Jenna von Oÿ.<ref>{{Cite book|last=Terrace|first=Vincent|url=https://books.google.com/books?id=1jUbAQAAIAAJ&q=Six+is+a+character+in+the+television+series+Blossom|title=Television Character and Story Facts: Over 110,000 Details from 1,008 Shows, 1945-1992|date=1993|publisher=McFarland & Company|isbn=978-0-89950-891-7|page=54|language=en|quote=Every Monday Blossom and Six ( who also...}}</ref>
*Six is the nickname of Kal Varrik, a central character in the television series ''Dark Matter'', played by Roger Cross.<ref>{{Cite web|title=Kal Varrick - Dark Matter|url=https://www.universeguide.com/character/kalvarrick|archive-url=https://web.archive.org/web/20200915161428/https://www.universeguide.com/character/kalvarrick|archive-date=September 15, 2020|access-date=2020-08-06|website=Universe Guide|language=en}}</ref>
*''Six'' is a History channel series that chronicles the operations and daily lives of SEAL Team Six.<ref>{{Cite web|date=2017-03-23|title=Six: A Review|url=http://quadcitiesdaily.com/?p=375705|access-date=2020-08-06|language=en-US}}</ref>
*''Six Feet Under'', an HBO series that ran from 2005 to 2011.<ref>{{Cite web|date=2019-10-16|title=The 100 Greatest TV Shows Of All Time|url=https://www.empireonline.com/movies/features/best-tv-shows-ever-2/|access-date=2020-08-06|website=Empire|language=en}}</ref>

===Movies===
*Number 6 (Teresa Palmer) is a character in the movie ''I Am Number Four'' (2011).<ref>{{Cite web|title=Character profile for Number 6 from I Am Number Four (Lorien Legacies, #1) (page 1)|url=https://www.goodreads.com/characters/57708-number-6|access-date=2020-08-06|website=www.goodreads.com}}</ref>
*''The 6th Day'' (2000), starring Arnold Schwarzenegger.<ref>{{Citation|title=The 6th Day (2000) - Roger Spottiswoode {{!}} Synopsis, Characteristics, Moods, Themes and Related {{!}} AllMovie|url=https://www.allmovie.com/movie/v214080|language=en-us|access-date=2020-08-06}}</ref>
*''The Sixth Sense'' (1999), written and directed by M. Night Shyamalan and starring Haley Joel Osment and Bruce Willis.<ref>{{Citation|title=The Sixth Sense (1999) - M. Night Shyamalan {{!}} Synopsis, Characteristics, Moods, Themes and Related {{!}} AllMovie|url=https://www.allmovie.com/movie/v180403|language=en-us|access-date=2020-08-06}}</ref>
*''Girl 6'' (1996), directed by Spike Lee.<ref>{{Citation|last=Lee|first=Spike|title=Girl 6|date=1996-03-22|url=https://www.imdb.com/title/tt0116414/|type=Comedy, Drama|others=Theresa Randle, Isaiah Washington, Spike Lee, Jenifer Lewis|publisher=Fox Searchlight Pictures, 40 Acres & A Mule Filmworks|access-date=2021-05-05}}</ref>

===Musicals===
* ''Six'' is a modern retelling of the lives of the six wives of [[Biography:Henry VIII|Henry VIII]] presented as a pop concert.<ref>{{Cite web|title=Six the Musical|url=https://www.sixthemusical.com/us-tour|access-date=2020-08-06|website=www.sixthemusical.com|language=en-GB}}</ref>

==Anthropology==
*The name of the smallest group of Cub Scouts and Guiding's equivalent Brownies, traditionally consisting of six people and is led by a "sixer".
*A coffin is traditionally buried six feet under the ground; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead<ref>{{Cite web|last=Rimes|first=Wendy|date=2016-04-01|title=The Reason Why The Dead Are Buried Six Feet Below The Ground|url=https://www.elitereaders.com/six-feet-under-ground-explanation/|access-date=2020-08-06|website=Elite Readers|language=en-US}}</ref>
*There are said to be no more than [[Social:Six degrees of separation|six degrees of separation]] between any two people on Earth.<ref>{{Cite web|title=Six Degrees of Peggy Bacon|url=https://www.aaa.si.edu/exhibitions/peggy-bacon|access-date=2020-08-06|website=www.aaa.si.edu|language=en}}</ref>
*In Western astrology, [[Unsolved:Virgo (astrology)|Virgo]] is the 6th astrological sign of the Zodiac<ref>{{Cite web|title=Virgo {{!}} constellation and astrological sign|url=https://www.britannica.com/place/Virgo|access-date=2020-08-06|website=Encyclopedia Britannica|language=en}}</ref>
*The Six Dynasties form part of Chinese history<ref>{{Cite book|last1=Wilkinson|first1=Endymion Porter|url=https://books.google.com/books?id=ERnrQq0bsPYC&pg=PA11|title=Chinese History: A Manual|last2=Wilkinson|first2=Scholar and Diplomat (Eu Ambassador to China 1994-2001) Endymion|date=2000|publisher=Harvard Univ Asia Center|isbn=978-0-674-00249-4|page=11|language=en}}</ref>
*Six is a lucky number in Chinese culture.<ref>{{Cite web|title=6 is a lucky number in Chinese culture - Google Search|url=https://www.google.com/search?safe=strict&tbm=bks&q=6+is+a+lucky+number+in+Chinese+culture|access-date=2020-08-06|website=www.google.com|quote=Two of the luckiest numbers in China are '6' and '8'.}}</ref>
*The Birmingham Six were a British miscarriage of justice, held in prison for 16 years.<ref>{{Cite news|last=Peirce|first=Gareth|date=2011-03-12|title=The Birmingham Six: Have we learned from our disgraceful past?|language=en-GB|work=The Guardian|url=https://www.theguardian.com/theguardian/2011/mar/12/gareth-peirce-birmingham-six|access-date=2020-08-06|issn=0261-3077}}</ref>
*"Six" is used as an informal slang term for the British Secret Intelligence Service, MI6.<ref>{{Cite book|last=Smith|first=Michael|url=https://books.google.com/books?id=qvCtAwAAQBAJ&q=SIX:+A+History+of+Britain's+Secret+Intelligence+Service|title=Six: The Real James Bonds 1909-1939|date=2011-10-31|publisher=Biteback Publishing|isbn=978-1-84954-264-7|language=en}}</ref>

==In other fields==
[[File:ICS Six.svg|right|thumb|66px|[[Engineering:International maritime signal flags|International maritime signal flag]] for 6]]
*Six-pack is a common form of packaging for six bottles or cans of drink (especially beer), and by extension, other assemblages of six items.<ref>{{Cite web|date=2018-09-19|title=Are Plastic Six-Pack Rings Still Ensnaring Wildlife?|url=https://www.nationalgeographic.com/environment/2018/09/news-plastic-six-pack-rings-alternatives-history/|archive-url=https://web.archive.org/web/20181118010815/https://www.nationalgeographic.com/environment/2018/09/news-plastic-six-pack-rings-alternatives-history/|url-status=dead|archive-date=November 18, 2018|access-date=2020-08-06|website=Environment|language=en}}</ref> Also, six is half a [[Dozen|dozen]].
*The number of dots in a [[Braille|braille]] cell.<ref>{{Cite web|title=What Is Braille? {{!}} American Foundation for the Blind|url=https://www.afb.org/blindness-and-low-vision/braille/what-braille|access-date=2020-08-06|website=www.afb.org}}</ref>
*[[Unsolved:Extrasensory perception|Extrasensory perception]] is sometimes called the "sixth sense".<ref>{{Cite book|last1=Walker|first1=Kathryn|url=https://books.google.com/books?id=ASnI9solIFoC&q=Extrasensory+perception+is+sometimes+called+the+%22sixth+sense%22.&pg=PA5|title=Mysteries of the Mind|last2=Innes|first2=Brian|date=2009|publisher=Crabtree Publishing Company|isbn=978-0-7787-4149-7|page=5|language=en|quote=this is sometimes called a " sixth sense "}}</ref>
*[[Company:Six Flags|Six Flags]] is an American company running amusement parks and theme parks in the U.S., Canada, and Mexico.<ref>{{Cite web|title=Six Flags Reopens With Enhanced Safety Protocols {{!}} IAAPA|url=https://www.iaapa.org/news/funworld/six-flags-reopens-enhanced-safety-protocols|access-date=2020-08-06|website=www.iaapa.org|language=en}}</ref>
*In the U.S. Army "Six" as part of a radio call sign is used by the commanding officer of a unit, while subordinate platoon leaders usually go by "One".<ref>
{{cite book
|last=Mason
|first=Robert
|title=Chickenhawk
|year=1983
|publisher=Corgi Books
|location=London
|isbn=978-0-552-12419-5
|page=141}}</ref> (For a similar example see also: Rainbow Six.)

== See also ==
*List of highways numbered 6
*Six degrees (disambiguation).

==References==
{{Reflist}}
*''The Odd Number 6'', JA Todd, Math. Proc. Camb. Phil. Soc. 41 (1945) 66–68
*''A Property of the Number Six'', Chapter 6, P Cameron, JH v. Lint, ''Designs, Graphs, Codes and their Links'' {{ISBN|0-521-42385-6}}
*Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 67 - 69

==External links==
*[https://web.archive.org/web/20161023134003/http://numdic.com/6 The Number 6]
*[http://www.positiveintegers.org/6 The Positive Integer 6]
*[http://primes.utm.edu/curios/page.php/6.html Prime curiosities: 6]


{{DEFAULTSORT:6 (Number)}}
[[Category:Integers]]
[[Category:6 (number)]]

{{Sourceattribution|6}}