8 (eight) is the natural number following 7 and preceding 9.

In mathematics

8 is: * a composite number, its proper divisors being , , and . It is twice 4 or four times 2. * a power of two, being 2 (two cubed), and is the first number of the form , being an integer greater than 1. * the first number which is neither prime nor semiprime. * the base of the octal number system, which is mostly used with

computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...

s. In octal, one digit represents three bits. In modern computers, a byte is a grouping of eight bits, also called an octet. * a Fibonacci number, being plus . The next Fibonacci number is . 8 is the only positive Fibonacci number, aside from 1, that is a perfect cube. * the only nonzero perfect power that is one less than another perfect power, by Mihăilescu's Theorem. * the order of the smallest non-abelian group all of whose subgroups are normal. * the dimension of the octonions and is the highest possible dimension of a normed division algebra. * the first number to be the aliquot sum of two numbers other than itself; the discrete biprime , and the square number . A number is divisible by 8 if its last three digits, when written in

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

, are also divisible by 8, or its last three digits are 0 when written in binary. A polygon with eight sides is an

octagon In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon. A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, whi ...

. The sides and

span Span may refer to: Science, technology and engineering * Span (unit), the width of a human hand * Span (engineering), a section between two intermediate supports * Wingspan, the distance between the wingtips of a bird or aircraft * Sorbitan es ...

of a regular octagon, or truncated square, are in silver ratio, and its circumscribing square has a side and diagonal length ratio of ; with both the silver ratio and the square root of two intimately interconnected through Pell numbers, where in particular the quotient of successive Pell numbers generates rational approximations for coordinates of a regular octagon. With a central angle of 45 degrees and an internal angle of 135 degrees, regular octagons are able to tessellate two-dimensional space alongside squares in the truncated square tiling, as well as fill a plane-vertex with a regular triangle and a regular icositetragon. The

Ammann–Beenker tiling In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann in the 1970s, or by the cut-and-project method as done independently by F. P. M. Beenker. Th ...

is a nonperiodic tesselation of prototiles that feature prominent octagonal ''silver'' eightfold symmetry, and is the two-dimensional orthogonal projection of the

8-8 duoprism In geometry of 4 dimensions or higher, a double prism or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an -polytope and an -polytope is an -polytope, wher ...

. In number theory, figurate numbers representing octagons are called octagonal numbers. A

cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only r ...

is a regular polyhedron with eight vertices that also forms the cubic honeycomb, the only regular honeycomb in three-dimensional space. Through various truncation operations, the cubic honeycomb generates eight other convex uniform honeycombs under the group

_3

. The octahedron, with eight equilateral triangles as faces, is the dual polyhedron to the cube and one of eight convex deltahedra. The stella octangula, or ''eight-pointed star'', is the only

stellation In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific el ...

with octahedral symmetry. It has eight triangular faces alongside eight vertices that form a cubic faceting, composed of two self-dual tetrahedra that makes it the simplest of five regular compound polyhedra. The cuboctahedron, on the other hand, is a rectified cube or rectified octahedron, and one of only two convex

quasiregular polyhedra In geometry, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular polygon, regular faces, which alternate around each vertex (geometry), vertex. They are vertex-transitive and edge-transitive, hence a step closer ...

. It contains eight equilateral triangular faces alongside six squares, whose first

is the cube-octahedron compound. The hexagonal prism, which classifies as an irregular octahedron that is a parallelohedron, like the cube, is able to tessellate space as a three-dimensional analogue of the hexagon. The gyrobifastigium, with four square faces and four triangular faces, is the only

Johnson solid In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...

that is able to tessellate space, while the

truncated octahedron In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagon, hexagons and 6 Squa ...

, also a parallelohedron, is the permutohedron of order four, with eight hexagonal faces alongside six squares that is likewise the only

Archimedean solid In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed ...

that can generate a honeycomb on its own.

Vertex-transitive In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in ...

semiregular polytopes whose facets are ''finite'' exist up through the 8th dimension. In the

third dimension Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...

, they include the Archimedean solids and the infinite family of uniform prisms and antiprisms, while in the

fourth dimension Fourth dimension may refer to: Science * Time in physics, the continued progress of existence and events * Four-dimensional space, the concept of a fourth spatial dimension * Spacetime, the unification of time and space as a four-dimensional con ...

, only the rectified 5-cell, the rectified 600-cell, and the snub 24-cell are semiregular polytopes. For dimensions

five 5 is a number, numeral, and glyph. 5, five or number 5 may also refer to: * AD 5, the fifth year of the AD era * 5 BC, the fifth year before the AD era Literature * ''5'' (visual novel), a 2008 visual novel by Ram * ''5'' (comics), an awa ...

through eight, the demipenteract and the k₂₁ polytopes 2₂₁, 3₂₁, and 4₂₁ are the only semiregular (

Gosset Gosset, founded in 1584, is the oldest wine house in Champagne. In 1584, Pierre Gosset, alderman of Aÿ and wine-grower, made still, mostly red, wines from the grapes he harvested from his own vines. In those days, two wines vied for pride of pl ...

) polytopes. Collectively, the k₂₁ family of polytopes contains eight figures that are rooted in the triangular prism, which is the simplest semiregular polytope that is made of three cubes and two equilateral triangles. It also includes one of only three semiregular Euclidean honeycombs: the