Mathematical properties
φ(12) = 4 τ(12) = 6 σ(12) = 28 π(12) = 5 μ(12) = 0 M(12) = 212 (twelve /ˈtwɛlv/ ( listen)) is the natural number following 11 and preceding 13. The product of the first three factorials, twelve is a superior highly composite number, divisible by 2, 3, 4, and 6. It is central to many systems of counting, including the Western calendar and units of time, and frequently appears in the Abrahamic religions.
The word "twelve" is the largest number with a singlesyllable name in English. Early Germanic numbers have been theorized to have been nondecimal: evidence includes the unusual phrasing of eleven and twelve, the former use of "hundred" to refer to groups of 120, and the presence of glosses such as "tentywise" or "tencount" in medieval texts showing that writers could not presume their readers would normally understand them that way.^{[1]}^{[2]}^{[3]} Such uses gradually disappeared with the introduction of Arabic numerals during the 12thcentury Renaissance.
It derives from the Old English twelf and tuelf, first attested in the 10thcentury Lindisfarne Gospels' Book of John.^{[n 1]}^{[5]} It has cognates in every Germanic language (e.g. German zwölf), whose ProtoGermanic ancestor has been reconstructed as *twaliƀi..., from *twa ("two") and suffix *lif or *liƀ of uncertain meaning.^{[5]} It is sometimes compared with the Lithuanian dvýlika, although lika is used as the suffix for all numbers from 11 to 19 (analogous to "teen").^{[5]} Every other IndoEuropean language instead uses a form of "two"+"ten", such as the Latin duōdecim.^{[5]} The usual ordinal form is "twelfth" but "dozenth" or "duodecimal" (from the Latin word) is also used in some contexts, particularly base12 numeration. Similarly, a group of twelve things is usually a "dozen" but may also be referred to as a "duodecad". The adjective referring to a group of twelve is "duodecuple".
As with eleven,^{[6]} the earliest forms of twelve are often considered to be connected with ProtoGermanic *liƀan or *liƀan ("to leave"), with the implicit meaning that "two is left" after having already counted to ten.^{[5]} The Lithuanian suffix is also considered to share a similar development.^{[5]} The suffix *lif has also been connected with reconstructions of the ProtoGermanic for ten.^{[6]}^{[7]}
While, as mentioned above, 12 has its own name in Germanic languages such as English, German, and Swedish. It is a compound number in many other languages, e.g. Italian dodici (but in Spanish and Portuguese, 16, and in French, 17 is the first compound number),^{[dubious – discuss]} Japanese 十二 jūni.^{[clarification needed]}
In prose writing, twelve, being the last singlesyllable numeral, is sometimes taken as the last number to be written as a word, and 13 the first to be written using digits. This is not a binding rule, and in English language tradition, it is sometimes recommended to spell out numbers up to and including either nine, ten or twelve, or even ninetynine or one hundred. Another system spells out all numbers written in one or two words (sixteen, twentyseven, fifteen thousand, but 372 or 15,001).^{[citation needed]} In German orthography, there used to be the widelyfollowed (but unofficial) rule of spelling out numbers up to twelve (zwölf). The Duden^{[year needed]} (the German standard dictionary) mentions this rule as outdated.
Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1, 2, 3, 4, 6 and 12. Twelve is also a highly composite number, the next one being twentyfour.^{[8]}
Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number.^{[9]} Since there is a subset of 12's proper divisors that add up to 12 (all of them but with 4 excluded), 12 is a semiperfect number.^{[10]}
If an odd perfect number is of the form 12k + 1, it has at least twelve distinct prime factors.
A twelvesided polygon is a dodecagon. A twelvefaced polyhedron is a dodecahedron. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. Twelve is a pentagonal number. The densest threedimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture). Twelve is also the kissing number in three dimensions.
Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant Δ(q) whose Fourier coefficients are given by the Ramanujan τfunction and which is (up to a constant multiplier) the 24th power of the Dedekind eta function. This fact is related to a constellation of interesting appearances of the number twelve in mathematics ranging from the value of the Riemann zeta function at −1 i.e. ζ(−1) = −1/12, the fact that the abelianization of SL(2,Z) has twelve elements, and even the properties of lattice polygons.
There are twelve Jacobian elliptic functions and twelve cubic distancetransitive graphs.
There are 12 Latin squares of size 3 × 3.
The duodecimal system (12_{10} [twelve] = 10_{12}), which is the use of 12 as a division factor for many ancient and medieval weights and measures, including hours, probably originates from Mesopotamia.
In base thirteen and higher bases (such as hexadecimal), twelve is represented as C. In base 10, the number 12 is a Harshad number.
Multiplication  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  50  100  1000  

12 × x  12  24  36  48  60  72  84  96  108  120  132  144  156  168  180  192  204  216  228  240  252  264  276  288  300  600  1200  12000 
Division  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  

12 ÷ x  12  6  4  3  2.4  2  1.714285  1.5  1.3  1.2  1.09  1  0.923076  0.857142  0.8  0.75  
x ÷ 12  0.083  0.16  0.25  0.3  0.416  0.5  0.583  0.6  0.75  0.83  0.916  1  1.083  1.16  1.25  1.3 
Exponentiation  1  2  3  4  5  6  7  8  9  10  11  12  13  

12^{x}  12  144  1728  20736  248832  2985984  35831808  429981696  5159780352  61917364224  743008370688  8916100448256  106993205379072  
x^{12}  1  4096  531441  16777216  244140625  2176782336  13841287201  68719476736  282429536481  1000000000000  3138428376721  8916100448256  23298085122481 
The number twelve has important symbolism attached to it in the world's cultures, generally representing perfection or entirety. Notably, twelve is the number of months in a year as traditionally represented both by the Western and the Chinese zodiac and the number of months in a solar calendar such as the Julian one. Ultimately, this is due to the number of full lunations in a solar year. In any case, the number twelve is recurring as the number of a "complete set" or "cosmic order" in religious, mythological and magical traditions since antiquity.^{[n 2]} Several sets of twelve cities are identified in history as a dodecapolis, the most familiar being the Etruscan League.
The significance is especially pronounced in the Hebrew Bible. Ishmael  the firstborn son of Abraham  had 12 sons/princes (Genesis 25:16), and Jacob also had 12 sons, who were the progenitors of the Twelve Tribes of Israel.^{[13]} This is reflected in Christian tradition, notably in the twelve Apostles. When Judas Iscariot was disgraced, a meeting was held (Acts) to add Saint Matthias to complete the number twelve once more. The Book of Revelation contains much numerical symbolism, and a lot of the numbers mentioned have 12 as a divisor. 12:1 mentions a woman—interpreted as the people of Israel, the Church or the Virgin Mary—wearing a crown of twelve stars (representing each of the twelve tribes of Israel). Furthermore, there are 12,000 people sealed from each of the twelve tribes of Israel, making a total of 144,000 (which is the square of 12 multiplied by a thousand). The "Twelve Days of Christmas" count the interval between Christmas and Epiphany. Eastern Orthodoxy observes twelve Great Feasts.
The number of twelve jurors in jury trials is depicted by Aeschylus in the Eumenides.In the play, the innovation is brought about by the goddess Athena, who summons twelve citizens to sit as jury. In English Common Law, the tradition of twelve jurors harks back to the 10thcentury law code introduced by Aethelred the Unready.
An example from Hinduism are the twelve Jyotirlinga in Shaiva tradition. The Sun god Surya has 12 names. Also, there are 12 Petals in Anahata or "heart chakra". The chief Norse god, Odin, had twelve sons. In the King Arthur Legend, Arthur is said to have subdued 12 rebel princes and to have won 12 great battles against Saxon invaders^{[14]}
In Twelver Shi'a Islam, there are twelve Imams, legitimate successors of the Islamic prophet, Muhammad. These twelve early leaders of Islam are—Ali, Hasan, Husayn, and nine of Husayn's descendants. Sura 12 in the Quran is sura Yusuf, narrating the story of the sons of Jacob.
12  Arabic  ១២  Khmer  ԺԲ  Armenian  

১২  Bangla  ΔΙΙ  Attic Greek  
יב  Hebrew 

Egyptian  
१२  Indian & Nepali (Devanāgarī)  十二  Chinese and Japanese  
௧௨  Tamil  Ⅻ  Roman and Etruscan  
๑๒  Thai  IIX  Chuvash  
౧౨  Telugu  ١٢  Urdu  
ιβʹ  Ionian Greek  ൧൨  Malayalam 
Movies with the number twelve or its variations in their titles include
Music Theory
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