In mathematics
- 26 is the seventh discrete semiprime () [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 II25,1 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.