4-Dimensional space

A 4-Dimensional Space is a space in which each point requires a quadruplet of numbers to describe its position. Examples of 4-dimensional spaces include a space with 3 spatial dimensions and 1 dimension used to find extents in our universe, spaces required to represent quaternions or coquaternions, and 4-manifolds with special curvatures.

It is the first hyperrealm, meaning a space with 4 or more dimensions.

Types of 4-Dimensional spaces

Examples of 4-dimensional spaces are listed below.

Tetraspherical

A tetrasphere is a four dimensional surface with positive curvature, and the four-dimensional equivalent of a 2-dimensional sphere. It bounds a 5-dimensional space called a pentorb.

Euclidean

A Euclidean flune is a four-dimensional space with zero curvature. It is a flune that follows the postulates of Euclidean geometry.

Hyperbolic

A hyperbolic flune is a four-dimensional flune with negative curvature.

Glomitubic

An infinite glomitube is a surface created from the Cartesian product of a three-dimensional glome and a Euclidean line.

Verses

A verse with four dimensions is called a fluneverse. Spatiotemporally, our universe is thought to be a fluneverse, though models of string theory made for phenomenology require more dimensions in our universe (multiverse, if you consider our universe to be the space localized on a D3 brane) to be consistent.

See Also

Dimensionality	Negative One	Zero	One	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	...	Aleph null
Hyperbolic space $\mathbb H^{n}$	—	—	—	Hyperbolic plane $\mathbb H^{2}$	Hyperbolic realm $\mathbb H^{3}$	Hyperbolic flune $\mathbb H^{4}$	Hyperbolic pentrealm $\mathbb H^{5}$	Hyperbolic hexealm $\mathbb H^{6}$	Hyperbolic heptealm $\mathbb H^{7}$	Hyperbolic octealm $\mathbb H^{8}$	Hyperbolic ennealm $\mathbb H^{9}$	Hyperbolic decealm $\mathbb H^{10}$	...	Hyperbolic omegealm $\mathbb H^{\aleph_0}$
Euclidean space $\R^n$	Null polytope $\emptyset$	Point $\mathbb R^{0}$	Euclidean line $\mathbb R^{1}$	Euclidean plane $\mathbb R^{2}$	Euclidean realm $\mathbb R^{3}$	Euclidean flune $\mathbb R^{4}$	Euclidean pentrealm $\mathbb R^{5}$	Euclidean hexealm $\mathbb R^{6}$	Euclidean heptealm $\mathbb R^{7}$	Euclidean octealm $\mathbb R^{8}$	Euclidean ennealm $\mathbb R^{9}$	Euclidean decealm $\mathbb R^{10}$	...	Euclidean omegealm $\mathbb R^{\aleph_0}$
Hypersphere $\mathbb S^{n}$		Point pair $\mathbb S^{0}$	Circle $\mathbb S^{1}$	Sphere $\mathbb S^{2}$	Glome $\mathbb S^{3}$	Tetrasphere $\mathbb S^{4}$	Pentasphere $\mathbb S^{5}$	Hexasphere $\mathbb S^{6}$	Heptasphere $\mathbb S^{7}$	Octasphere $\mathbb S^{8}$	Enneasphere $\mathbb S^{9}$	Dekasphere $\mathbb S^{10}$	...	Omegasphere $\mathbb S^{\aleph_0}$