14 (number)

14 (fourteen) is a natural number following 13 and preceding 15. In relation to the word "four" (4), 14 is spelled "fourteen". 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.