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A 2-Dimensional Space is a space in which every position can be described using a pair of numbers, such as with a complex number.

## Types of 2-Dimensional Space

The types of a two-dimensional space can be sorted according to their curvature. Roughly, positive curvature causes parallel lines to meet, and negative curvature causes parallel lines to diverge.

### Spherical

The spherical plane has a positive curvature, and can be thought of as the two-dimensional space being a sphere, on the surface of a ball. Two parallel lines will eventually wrap around the sphere and meet again, and similarly walking in a straight line will eventually return an entity in a spherical space to its original location.

### Euclidean

The Euclidean plane has a zero curvature, and is the ordinary flat plane that follows the postulates of Euclidean geometry.

### Hyperbolic

The hyperbolic plane has a negative curvature. This means that two parallel lines will diverge, giving them the name ultraparallel.

## Verses

A two-dimensional verse is called a planeverse.

Dimensionality Negative First Zeroth First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth Eleventh Twelfth Thirteenth Fourteenth Fifteenth Sixteenth ... Omegath
Hyperbolic space

$\mathbb H^{n}$

Null polytope

$\emptyset$

Point

$\mathbb H^{0}$

Hyperbola

$\mathbb H^{1}$

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

$\mathbb H^{13}$

$\mathbb H^{14}$

$\mathbb H^{15}$

$\mathbb H^{16}$

... Hyperbolic omegealm

$\mathbb H^{\aleph_0}$

Euclidean space

$\mathbb R^{n}$

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 hendecealmverse

$\mathbb R^{11}$

Euclidean dodecealmverse

$\mathbb R^{12}$

Euclidean tridecealm

$\mathbb R^{13}$

$\mathbb R^{14}$

$\mathbb R^{15}$

$\mathbb R^{16}$

... Euclidean omegealm

$\mathbb R^{\aleph_0}$

Hypersphere

$\mathbb S^{n}$

Null polytope

$\emptyset$

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

$\mathbb S^{13}$

$\mathbb S^{14}$

$\mathbb S^{15}$
$\mathbb S^{16}$
$\mathbb S^{\aleph_0}$