**Spatial dimensions** are the dimensions used in many fields of mathematics.

## DimensionsEdit

**Dimension 0—a mathematical point**Edit

Dimension 0 is literally a point in space. Points can be described by coordinates, (x, y), and graphed on a coordinate plane. Since a 0-dimensional object has neither length, width, nor depth, it is immeasurable.

Vertices*: 2^{0} = 1

Total Possible Lines†: (1 * 0)/2 = 0

**Dimension 1—a line**Edit

Dimension 1 is any two 0-dimensional points connected with a line, ray, or segment. A 1-dimensional object can only be measured in length. If you were a 0-dimensional object looking at a 1-dimensional line, you would see a point that appears and disappears where the line is. In other words, the line would appear in cross-sections of points. 1-dimensional lines can stretch for an eternity.

Vertices: 2^{1} = 2

Total Possible Lines: (2 * 1)/2 = 1

**Dimension 2—a flat plane**Edit

Dimension 2 is at least two 1-dimensional lines that either connect or intersect to form a plane. A plane has width and length. To a 1-dimensional line, a plane appears as both lines and points.

Vertices: 2^{2} = 4

Total Possible Lines: (4 * 3)/2 = 6

**Dimension 3—3-dimensional space**Edit

Dimension 3 is at least two planes that either connect or intersect to form 3-dimensional space. 3-dimensional space has length, width, and height. A 2-dimensional plane would see space as a cross section of definite 2-dimensional shapes.

Vertices: 2^{3} = 8

Total Possible Lines: (8 * 7)/2 = 28

**Dimension 4—4-dimensional space**Edit

4-dimensional space is made when at least two 3-dimensional spaces converge and/or intersect. Imagining this dimension and onwards is notoriously difficult for our minds to conjure, with each new dimension becoming increasingly complex and consequentially harder to conjure.

Vertices: 2^{4} = 16

Total Possible Lines: (16 * 15)/2 = 120

**Dimensions 5 and Above—***x*-dimensional spaceEdit

*x*-dimensional space

Each dimension after dimension 4 is a more complex version of space than the previous. For example, 5-dimensional space is made by intersecting multiple 4-dimensional spaces, and 6-dimensional space is made by intersecting multiple 5-dimensional spaces, and so on and so forth.

For dimension 5,

Vertices: 2^{5} = 32

Total Possible Lines: (32 * 31)/2 = 496

For dimension 6,

Vertices: 2^{6} = 64

Total Possible Lines: (64 * 63)/2 = 2,016

For dimension 7,

Vertices: 2^{7} = 128

Total Possible Lines: (128 * 127)/2 = 8,128

For dimension 8,

Vertices: 2^{8} = 256

Total Possible Lines: (256 * 255)/2 = 32,640

For dimension 9,

Vertices: 2^{9} = 512

Total Possible Lines: (512 * 511)/2 = 130,816

(For more info on these calculations, consult notes * and †.)

## See AlsoEdit

## NotesEdit

*You can calculate the number of vertices an *x*-dimensional cube has with 2^{x}.

†All the possible unique lines that can be drawn between each of the vertices. You can calculate this using $ \frac{(2^x)(2^x-1)}{2}\, $, where *x* is the number of dimensions.