20 (twenty; Roman numeral XX) is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.^[1][2]

In mathematics

An icosahedron has twenty triangular faces.

Twenty is a pronic number, as it is the product of consecutive integers, namely 4 and 5.^[3] It is the third composite number to be the product of a squared prime and a prime, and also the second member of the 2² × q family in this form.

20 has an aliquot sum of 22; a semiprime, within an aliquot sequence of four composite numbers (20, 22, 14, 10, 8) that belong to the prime 7-aliquot tree.

• 20 is the smallest primitive abundant number.^[4]
• 20 is the third tetrahedral number.^[5]
• 20 is the basis for vigesimal number systems.^[6]
• 20 is the number of parallelogram polyominoes with 5 cells.^[7]
• 20 is the number of moves (quarter or half turns) required to optimally solve a Rubik's Cube in the worst case.^[8][9]
• 20 is the length of a side of the fifth smallest right triangle that forms a primitive Pythagorean triple, (20,21,29).^[10] This is the second Pythagorean triple ${\displaystyle (a,b,c)}$ that can be formed using Pell numbers where ${\displaystyle a}$ and ${\displaystyle b}$ are one unit apart.^{[lower-alpha 1]}
• 20 is the smallest non-trivial decimal neon number equal to the sum of its digits when raised to the thirteenth power (20¹³ = 8192 × 10¹³).

Gelfond's constant and pi very nearly have a difference equal to twenty:

$${\displaystyle e^{\pi }-\pi \;\approx \;20}$$

differing only by about ${\displaystyle -0.000900020811\ldots }$ from an integer value.^[11][12]

There are twenty edge-to-edge 2-uniform tilings by convex regular polygons, which are uniform tessellations of the plane containing 2 orbits of vertices.^[13][14]

The largest number of faces a Platonic solid can have is twenty faces, which make up a regular icosahedron.^[15] A dodecahedron, on the other hand, has twenty vertices, likewise the most a regular polyhedron can have.^[16] There are a total of 20 regular and semiregular polyhedra, aside from the infinite family of semiregular prisms and antiprisms that exists in the third dimension: the 5 Platonic solids, and 15 Archimedean solids (including chiral forms of the snub cube and snub dodecahedron). There are also four uniform compound polyhedra that contain twenty polyhedra (UC₁₃, UC₁₄, UC₁₉, UC₃₃), which is the most any such solids can have; while another twenty uniform compounds contain five polyhedra. The compound of twenty octahedra can be obtained by orienting two pairs of compounds of ten octahedra, which can also coincide to yield a regular compound of five octahedra.

In total, there are 20 semiregular polytopes that only exist up through the 8th dimension, which include 13 Archimedean solids and 7 Gosset polytopes (without counting enantiomorphs, or semiregular prisms and antiprisms).

Bring's curve is a Riemann surface of genus four, whose fundamental polygon is a regular hyperbolic twenty-sided icosagon, with an area equal to ${\displaystyle 12\pi }$ by the Gauss-Bonnet theorem.^[17]

The Happy Family of sporadic groups is made up of twenty finite simple groups that are all subquotients of the friendly giant, the largest sporadic group. The largest supersingular prime factor that divides the order of the friendly giant is 71, which is the 20th indexed prime number. Both 71 and 20 represent self-convolved Fibonacci numbers, respectively the seventh and fifth members ${\displaystyle j}$ in this sequence ${\displaystyle F_{j}^{2}}$.^[18][19]

In science

• The atomic number of calcium
• The third magic number in physics
• The International Astronomical Union shower number for Coma Berenicids

As an indefinite number

• A 'score' is a group of 20 (often used in combination with a cardinal number, e.g. fourscore to mean 80),^[21] but also often used as an indefinite number^[22] (e.g. the newspaper headline "Scores of Typhoon Survivors Flown to Manila").^[23]

In sports

A standard dartboard is laid out as 20 sectors.

• Twenty20 is a form of limited overs cricket where each team plays only 20 overs.^[24]
• A standard dartboard is laid out as 20 sectors.
• The Kentucky Derby currently has a maximum field of 20 horses.^[25]
• In rugby union, 20 national teams currently qualify for each edition of the men's Rugby World Cup.
• In chess, 20 is the number of legal moves for each player in the starting position.^[26]
• In Australian rules football, most games consist of four 20-minute quarters.^[27]
• Under NCAA men's basketball rules, games consist of 20-minute halves.^[28]
• Ice hockey games are played in three 20-minute periods.^[29]
• The current Formula 1 field size is 20.
• 20 was used by Tony Stewart and Joe Gibbs Racing to win the 2002 and 2005 NASCAR Cup Series championships. It is currently used by Christopher Bell.

Age 20

• In many disciplines of developmental psychology, adulthood starts at age 20.^[30]
• Formerly the age of majority in Japan and in Japanese tradition.^[31]
• Age 20 is the age at which Levites in the time of King David were allowed "to do the work for the service of the house of the Lord", the Temple in Jerusalem (see First Chronicles Chapter 23, verses 24 and 27). In the time of Ezra and Nehemiah, following the Babylonian captivity, it was Levites from the age of 20 upwards who were assigned "to oversee the work of the house of the LORD" (Ezra Chapter 3, verse 8).

Music

In other fields

• +20 is the code for international direct dial phone calls to Egypt.^[82]
• CB slang for a place, being short for the ten-code "10–20" meaning "What is your location?"^[83]
• 20/20 is a primetime newsmagazine program on ABC, which in turn is taken from the expression for normal eyesight (20/20 vision).
• 020 is the ISO 3166-1 numeric 3 digit country code for Andorra.^[84]
• The UIC Country Code for Russia identifying member countries of the International Union of Railways (UIC).
• 20 is the value of the letter J when computing the check digit in the serial number of an intermodal (shipping) container, as defined by ISO 6346.
• In Hebrew numerals, the letter Kaph (כ) represents twenty;^[85] see also gematria, the Hebrew system of numerology. Similarly the Arabic letter kāf (ك) represents twenty in the Abjad numerals.
• The number of questions in the game Twenty Questions.^[86]

See also

• List of highways numbered 20

References

External links

Look up twenty in Wiktionary, the free dictionary.

• Media related to 20 (number) at Wikimedia Commons