26 (number)

"Number 26" and "XXVI" redirect here. For the bank, see N26. For the company, see XXVI Holdings.

26 (twenty-six) is the natural number following 25 and preceding 27.

← 25 26 27 →
← 20 21 22 23 24 25 26 27 28 29 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	twenty-six
Ordinal	26th (twenty-sixth)
Factorization	2 × 13
Divisors	1, 2, 13, 26
Greek numeral	ΚϚ´
Roman numeral	XXVI, xxvi
Binary	110102
Ternary	2223
Senary	426
Octal	328
Duodecimal	2212
Hexadecimal	1A16

In mathematics

Poster designed to depict the speciality of the number 26

• 26 is the seventh discrete semiprime (${\displaystyle 2\times 13}$)^[1] and the fifth with 2 as the lowest non-unitary factor thus of the form (2.q), where q is a higher prime.
• 26 is the smallest even number n such that both n + 1 and n − 1 are composite.
• With an aliquot sum of 16, within an aliquot sequence of five composite numbers (26,16,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
• 26 is the only integer that is one greater than a square (5² + 1) and one less than a cube (3³ − 1).^[2]
• 26 is a telephone number, specifically, the number of ways of connecting 5 points with pairwise connections.^[3]
• There are 26 sporadic groups.^[4]
• The 26-dimensional Lorentzian unimodular lattice II_25,1 plays a significant role in sphere packing problems and the classification of finite simple groups. In particular, the Leech lattice is obtained in a simple way as a subquotient.
• 26 is the smallest number that is both a nontotient and a noncototient number.
• 26 is the number of permutations of {a, b, c, d, e} with only one ascent.^[5][a]
• There are 26 faces of a rhombicuboctahedron.^[6]
• The gyroelongated square cupola (J₂₃), elongated square gyrobicupola (J₃₇), gyroelongated triangular bicupola (J₄₄), and snub square antiprism (J₈₅) each have 26 faces.^[7]
• When a 3 × 3 × 3 cube is made of 27 unit cubes (e.g. Rubik's Cube), 26 of them are viewable as the exterior layer.
• A cube has 26 elements: 6 faces, 12 edges, and 8 vertices.
• A 26-sided polygon is called an icosihexagon.^[8]
• φ(26) = 12 = φ(σ(26)).^[9]

Properties of its positional representation in certain radixes

Twenty-six is a repdigit in bases three (222₃) and twelve (22₁₂).

In base ten, 26 is the smallest positive integer that is not a palindrome to have a square (26² = 676) that is a palindrome.

In religion

• 26 is the gematric number, being the sum of the Hebrew characters (Hebrew: יהוה) being the name of the god of Israel – YHWH (Yahweh).
• 26 is also the gematric number for GOD with the corresponding substitutions in English (i.e. A=1, B=2, C=3, and so on)
• In the Tenrikyo religion of Japan, 26 is frequently used, since it marks the lunar calendar date of its founder Nakayama Miki's first divine revelation and also her death.

In science

• Messier 26 is an open cluster of stars in the southern constellation of Scutum.
• NGC 26 is a spiral galaxy in the Pegasus constellation.
• The maximum time difference between two timezones is 26 hours.