14 (fourteen) is a natural number following 13 and preceding 15.
In relation to the word "four" (4), 14 is spelled "fourteen".
In mathematics
Fourteen is the seventh composite number. It is specifically, the third distinct Semiprime, it also being the 3rd of the form (2.q) , where q is a higher prime.
It has an aliquot sum of 8, within an aliquot sequence of two composite numbers (14,8,7,1,0) to the Prime in the 7-aliquot tree.
14 is the first member of the first cluster of two discrete semiprimes (14, 15) the next such cluster is (21, 22).
It is the lowest even for which the equation has no solution, making it the first even nontotient.
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.
14 is the third stella octangula number, and the second square pyramidal number.
14 is also the fourth Companion Pell number, and the fifth Catalan number.
According to the Shapiro inequality, 14 is the least number such that there exist , , , where:
with and
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.
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.
The regular tetrahedron, 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.p.16 Furthermore, if three tetrahedra are joined at two separate opposing edges and made into a single flexible polyhedron, called a 2-dof flexible polyhedron, each hinge will only have a total range of motion of 14 degrees.p.139
There are fourteen possible Bravais lattices that fill three-dimensional space.
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 by the Gauss-Bonnet theorem.
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 , and holds a compact form homeomorphic to the zero divisors with entries of unit norm in the sedenions, .
In science
Chemistry
The atomic number of silicon
The approximate atomic weight of nitrogen
The maximum number of electrons that can fit in an f sublevel
Group 14 elements in the periodic table.
Astronomy
Messier object M14, a magnitude 9.5 globular cluster in the constellation Ophiuchus The New General Catalogue object NGC 14, a magnitude 12.5 irregular galaxy in the constellation Pegasus