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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 Zero One Two Three Four Five Six Seven Eight Nine Ten Eleven Twelve Thirteen Fourteen Fifteen Sixteen ... 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 hendecealm

$\mathbb H^{11}$

Hyperbolic dodecealm

$\mathbb H^{12}$

Hyperbolic tridecealm

$\mathbb H^{13}$

Hyperbolic tetradecealm

$\mathbb H^{14}$

Hyperbolic pentadecealm

$\mathbb H^{15}$

Hyperbolic hexadecealm

$\mathbb H^{16}$

... Hyperbolic omegealm

$\mathbb H^{\aleph_0}$

Euclidean space

$\mathbb R^{n}$

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 hendecealmverse

$\mathbb R^{11}$

Euclidean dodecealmverse

$\mathbb R^{12}$

Euclidean tridecealm

$\mathbb R^{13}$

Euclidean tetradecealm

$\mathbb R^{14}$

Euclidean pentadecealm

$\mathbb R^{15}$

Euclidean hexadecealm

$\mathbb R^{16}$

... 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

$\mathbb S^{10}$

Hendekasphere

$\mathbb S^{11}$

Dodekasphere

$\mathbb S^{12}$

Tridekasphere

$\mathbb S^{13}$

Tetradekasphere

$\mathbb S^{14}$

Pentadekasphere

$\mathbb S^{15}$

Hexadekasphere

$\mathbb S^{16}$

... Omegasphere

$\mathbb S^{\aleph_0}$