.
Fourteen is the seventh
composite number.
Properties 14 is the third distinct
semiprime, being the third of the form 2 \times q (where q is a higher prime). More specifically, it is the first member of the second cluster of two discrete
semiprimes (14,
15); the next such cluster is (
21,
22), members whose sum is the fourteenth prime number,
43. 14 has an
aliquot sum of
10, within an
aliquot sequence of two composite numbers (14,
10,
8,
7,
1, 0) in the prime
7-aliquot tree. 14 is the third
companion Pell number and the fourth
Catalan number. It is the lowest even n for which the
Euler totient \varphi(x) = n has no solution, making it the first even
nontotient. According to the
Shapiro inequality, 14 is the least number n such that there exist x_{1}, x_{2}, x_{3}, where: :\sum_{i=1}^{n} \frac{x_i}{x_{i+1}+x_{i+2}} with x_{n+1} = x_{1} and x_{n+2} = x_{2}. A
set of
real numbers to which it is applied
closure and
complement operations in any possible sequence generates
14 distinct sets. This holds even if the reals are replaced by a more general
topological space; see
Kuratowski's closure-complement problem. There are fourteen
even numbers that cannot be expressed as the sum of two odd
composite numbers: :\{2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 26, 28, 32, 38\} where 14 is the seventh such number.
Polygons 14 is the number of
equilateral triangles that are formed by the
sides and
diagonals of a
regular six-sided
hexagon. In a
hexagonal lattice, 14 is also the number of fixed two-dimensional
triangular-celled
polyiamonds with four cells. 14 is the number of
elements in a
regular heptagon (where there are seven
vertices and edges), and the total number of
diagonals between all its vertices. There are fourteen polygons that can fill a
plane-vertex tiling, where five polygons tile the plane
uniformly, and nine others only tile the plane alongside irregular polygons. is a regular hyperbolic 14-sided
tetradecagon, with an area of 8\pi. The
Klein quartic is a compact
Riemann surface of genus 3 that has the largest possible
automorphism group order of its kind (of order
168) whose fundamental domain is a regular hyperbolic 14-sided
tetradecagon, with an area of 8\pi by the
Gauss-Bonnet theorem.
Solids Several distinguished
polyhedra in
three dimensions contain fourteen
faces or
vertices as
facets: • The
cuboctahedron, one of two
quasiregular polyhedra, has 14 faces and is the only
uniform polyhedron with
radial equilateral symmetry. • The
rhombic dodecahedron,
dual to the cuboctahedron, contains 14 vertices and is the only
Catalan solid that can
tessellate space. • The
truncated octahedron contains 14 faces, is the
permutohedron of order four, and the only
Archimedean solid to tessellate space. • The
dodecagonal prism, which is the largest
prism that can tessellate space alongside other uniform prisms, has 14 faces. • The
Szilassi polyhedron and its dual, the
Császár polyhedron, are the simplest
toroidal polyhedra; they have 14 vertices and 14 triangular faces, respectively. •
Steffen's polyhedron, the simplest
flexible polyhedron without self-crossings, has 14 triangular faces. A regular
tetrahedron cell, the simplest
uniform polyhedron and
Platonic solid, is made up of a total of
14 elements: 4
edges, 6 vertices, and 4 faces. • Szilassi's polyhedron and the tetrahedron are the only two known polyhedra where each face shares an edge with each other face, while Császár's polyhedron and the tetrahedron are the only two known polyhedra with a continuous
manifold boundary that do not contain any
diagonals. • Two tetrahedra that are joined by a common edge whose four adjacent and opposite faces are replaced with two specific seven-faced
crinkles will create a new flexible polyhedron, with a total of 14 possible
clashes where faces can meet.pp.10-11,14 This is the second simplest known triangular flexible polyhedron, after Steffen's polyhedron. the simplest of the ninety-two
Johnson solids is the
square pyramid J_{1}. There are a total of fourteen
semi-regular polyhedra, when the
pseudorhombicuboctahedron is included as a non-
vertex transitive Archimedean solid (a lower class of polyhedra that follow the five Platonic solids). Fourteen possible
Bravais lattices exist that fill three-dimensional space.
G2 The
exceptional Lie algebra G2 is the simplest of five such algebras, with a minimal
faithful representation in fourteen dimensions. It is the
automorphism group of the
octonions \mathbb {O}, and holds a compact form
homeomorphic to the
zero divisors with entries of
unit norm in the
sedenions, \mathbb {S}.
Riemann zeta function The
floor of the
imaginary part of the first non-trivial zero in the
Riemann zeta function is 14, in equivalence with its
nearest integer value, from an approximation of 14.1347251417\ldots ==In religion and mythology==