:6

A six-sided polygon is a hexagon, one of the three regular polygons capable of tiling the plane. A hexagon also has 6 edges as well as 6 internal and external angles.

6 is the second smallest composite number.{{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}} It is also the first number that is the sum of its proper divisors, making it the smallest perfect number.{{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] }} It is also the only perfect number that doesn't have a digital root of 1.{{Cite web |last=Weisstein |first=Eric W. |title=Perfect Number |url=https://mathworld.wolfram.com/PerfectNumber.html |access-date=2025-03-20 |website=mathworld.wolfram.com |language=en}} 6 is the first unitary perfect number, since it is the sum of its positive proper unitary divisors, without including itself. Only five such numbers are known to exist.{{Cite OEIS|A002827|Unitary perfect numbers|access-date=2016-06-01}} 6 is the largest of the four all-Harshad numbers.{{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}}

6 is the 2nd superior highly composite number,{{Cite web |title=A002201 - OEIS |url=https://oeis.org/A002201 |access-date=2024-11-28 |website=oeis.org}} the 2nd colossally abundant number,{{Cite web |title=A004490 - OEIS |url=https://oeis.org/A004490 |access-date=2024-11-28 |website=oeis.org}} the 3rd triangular number,{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}} the 4th highly composite number,{{Cite web |title=A002182 - OEIS |url=https://oeis.org/A002182 |access-date=2024-11-28 |website=oeis.org}} a pronic number,{{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}} a congruent number,{{Cite OEIS|A003273|Congruent numbers|access-date=2016-06-01}} a harmonic divisor number,{{Cite web |title=A001599 - OEIS |url=https://oeis.org/A001599 |access-date=2024-11-28 |website=oeis.org}} and a semiprime.{{Cite OEIS|A001358 |Semiprimes (or biprimes): products of two primes. |access-date=2023-08-03 }} 6 is also the first Granville number, or $\backslash mathcal\{S\}$-perfect number. A Golomb ruler of length 6 is a "perfect ruler".Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 72

The six exponentials theorem guarantees that under certain conditions one of a set of six exponentials is transcendental.{{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}} The smallest non-abelian group is the symmetric group $\backslash mathrm\; \{S\_\{3\}\}$ which has 3! = 6 elements. 6 the answer to the two-dimensional kissing number problem.{{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}}

File:120px-Hexahedron-slowturn.gif, with six faces]]

A cube has 6 faces. A tetrahedron has 6 edges. In four dimensions, there are a total of six convex regular polytopes.

In the classification of finite simple groups, twenty of twenty-six sporadic groups in the happy family are part of three families of groups which divide the order of the friendly giant, the largest sporadic group: five first generation Mathieu groups, seven second generation subquotients of the Leech lattice, and eight third generation subgroups of the friendly giant. The remaining six sporadic groups do not divide the order of the friendly giant, which are termed the pariahs (Ly, O'N, Ru, J₄, J₃, and J₁).{{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 }}

{{lang|grc-Latn|Hexa}} is classical Greek for "six". Thus:

• "Hexadecimal" combines {{lang|grc-Latn|hexa-}} with the Latinate {{lang|la|decimal}} to name a number base of 16{{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}}
• A hexagon is a regular polygon with six sides{{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}}
• {{lang|fr|L'Hexagone}} is a French nickname for the continental part of Metropolitan France for its resemblance to a regular hexagon
• A hexahedron is a polyhedron with six faces, with a cube being a special case{{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}}
• Hexameter is a poetic form consisting of six feet per line
• A "hex nut" is a nut with six sides, and a hex bolt has a six-sided head
• The prefix "{{lang|grc-Latn|hexa-}}" also occurs in the systematic name of many chemical compounds, such as hexane which has 6 carbon atoms ({{chem2|C6H14}}).

Sex- is a Latin prefix meaning "six". Thus:

• Senary is the ordinal adjective meaning "sixth"{{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}}
• People with sexdactyly have six fingers on each hand
• The measuring instrument called a sextant got its name because its shape forms one-sixth of a whole 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.{{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 }}{{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}}

The SI prefix for 1000⁶ is exa- (E), and for its reciprocal atto- (a).

File:Edicts of Ashoka numerals.jpg {{Circa|250 BCE}}. These are Brahmi numerals, ancestors of Hindu-Arabic numerals.]]

File:Ashoka Brahmi numerals 256.jpg 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 India, which are first known from the Edicts of Ashoka {{Circa|250 BCE}}.{{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}}{{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}}{{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}}{{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}} 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.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

On the seven-segment displays 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 typefaces, in typefaces with text figures the character for the digit 6 usually has an ascender, as, for example, in 52px.{{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 )}}

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.

File:Bienenwabe mit Eiern und Brut 5.jpg are six-sided.]]

File:Benzene structure.png of benzene has a ring of six carbon and six hydrogen atoms.]]

• The sixfold symmetry of snowflakes arises from the hexagonal crystal structure of ordinary ice.{{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}}

• 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.{{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}}
• Six is a lucky number in Chinese culture."Chinese Numbers 1 to 10 | maayot". maayot • Bite-size daily Chinese stories. 2021-11-22. Retrieved 2025-01-17.
• "Six" is used as an informal slang term for the British Secret Intelligence Service, MI6.{{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}}

• Six degrees (disambiguation).

{{Reflist}}

• {{cite journal

| title=The 'odd' number six

| last1=Todd | first1=J. A. | authorlink1=J. A. Todd

| journal=Mathematical Proceedings of the Cambridge Philosophical Society

| volume=41

| issue=1

| date=1945

| pages=66–68

| doi=10.1017/S0305004100022374}}

• 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

{{Wiktionary|six}}

• [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]

{{Integers|zero}}

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Category:Integers

Category:6 (number)