In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space.
More generally the term may refer to an eight-dimensional vector space over any field, such as an eight-dimensional complex vector space, which has 16 real dimensions.
It may also refer to an eight-dimensional manifold such as an 8-sphere, or a variety of other geometric constructions.
Each uniform polytope is defined by a ringed Coxeter-Dynkin diagram.
The 7-sphere or hypersphere in eight dimensions is the seven-dimensional surface equidistant from a point, e.g. the origin.
The kissing number problem has been solved in eight dimensions, thanks to the existence of the 421 polytope and its associated lattice.
A normed division algebra additionally must be finite-dimensional, and have the property that every non-zero vector has a unique multiplicative inverse.
Hurwitz's theorem prohibits such a structure from existing in dimensions other than 1, 2, 4, or 8.
, or "biquaternions," are an eight-dimensional algebra dating to William Rowan Hamilton's work in the 1850s.
It has also been proposed as a practical or pedagogical tool for doing calculations in special relativity, and in that context goes by the name Algebra of physical space (not to be confused with the Spacetime algebra, which is 16-dimensional.)