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A line segment, also known as an interval or closed interval, is 2 connected points.

It can be considered as being the solid interior of the 0-dimensional hypersphere, the point pair.

A circle can be made by rotating a line segment around the middle axis.

People often refer to it as a line. A proper line has infinite length. They refer to a line segment when they mean line.

A line segment is actually made of an infinite number of points as the line connecting the two points is made up of an infinite number of points.

Symbols

The line segment can be given a symbol in two ways:

  • x - two equivalent vertices
  • oo&#x - two distinct vertices

Hypervolumes

Subfacets

Radii

  • Vertex radius: $ 1/2l $

Equations

All points on the surface of a line, a point pair can be given by the equation

$ x^2 = l^2/4 $

where l is the length of the line segment.

Vertex coordinates

A line segment of length 2 has the vertex coordinates (±1).

Notations

  • Toratopic notation: $ | $
  • Tapertopic notation: $ 1 $

Related shapes

  • Dual: self dual
  • Vertex figure: Point

See also

First Dimension

Dimensionality Negative One Zero One Two Three Four Five Six Seven Eight Nine Ten Eleven Twelve Thirteen Fourteen Fifteen Sixteen ... Aleph null
Simplex

$ \{3^{n-1}\} $

Null polytope

$ )( $
$ \emptyset $

Point

$ () $
$ \mathbb{B}^0 $

Line segment

$ \{\} $
$ \mathbb{B}^1 $

Triangle

$ \{3\} $

Tetrahedron

$ \{3^2\} $

Pentachoron

$ \{3^3\} $

Hexateron

$ \{3^4\} $

Heptapeton

$ \{3^5\} $

Octaexon

$ \{3^6\} $

Enneazetton

$ \{3^7\} $

Decayotton

$ \{3^8\} $

Hendecaxennon

$ \{3^9\} $

Dodecadakon

$ \{3^{10}\} $

Tridecahendon

$ \{3^{11}\} $

Tetradecadokon

$ \{3^{12}\} $

Pentadecatradakon

$ \{3^{13}\} $

Hexadecatedakon

$ \{3^{14}\} $

Heptadecapedakon

$ \{3^{15}\} $

... Omegasimplex
Cross

$ \{3^{n-2},4\} $

Square

$ \{4\} $

Octahedron

$ \{3, 4\} $

Hexadecachoron

$ \{3^2, 4\} $

Pentacross

$ \{3^3, 4\} $

Hexacross

$ \{3^4, 4\} $

Heptacross

$ \{3^5, 4\} $

Octacross

$ \{3^6, 4\} $

Enneacross

$ \{3^7, 4\} $

Dekacross

$ \{3^8, 4\} $

Hendekacross

$ \{3^9, 4\} $

Dodekacross

$ \{3^{10}, 4\} $

Tridekacross

$ \{3^{11}, 4\} $

Tetradekacross

$ \{3^{12}, 4\} $

Pentadekacross

$ \{3^{13}, 4\} $

Hexadekacross

$ \{3^{14}, 4\} $

... Omegacross
Hydrotopes

$ \{3^{n-2}, 5\} $

Pentagon

$ \{5\} $

Icosahedron

$ \{3, 5\} $

Hexacosichoron

$ \{3^2, 5\} $

Order-5 pentachoric tetracomb

$ \{3^3, 5\} $

Order-5 hexateric pentacomb

$ \{3^4, 5\} $

...
Hypercube

$ \{4, 3^{n-2}\} $

Square

$ \{4\} $

Cube

$ \{4, 3\} $

Tesseract

$ \{4, 3^2\} $

Penteract

$ \{4, 3^3\} $

Hexeract

$ \{4, 3^4\} $

Hepteract

$ \{4, 3^5\} $

Octeract

$ \{4, 3^6\} $

Enneract

$ \{4, 3^7\} $

Dekeract

$ \{4, 3^8\} $

Hendekeract

$ \{4, 3^9\} $

Dodekeract

$ \{4, 3^{10}\} $

Tridekeract

$ \{4, 3^{11}\} $

Tetradekeract

$ \{4, 3^{12}\} $

Pentadekeract

$ \{4, 3^{13}\} $

Hexadekeract

$ \{4, 3^{14}\} $

... Omegeract
Cosmotopes

$ \{5, 3^{n-2}\} $

Pentagon

$ \{5\} $

Dodecahedron

$ \{5, 3\} $

Hecatonicosachoron

$ \{5, 3^2\} $

Order-3 hecatonicosachoric tetracomb

$ \{5, 3^3\} $

Order-3-3 hecatonicosachoric pentacomb

$ \{5, 3^4\} $

...
Hyperball

$ \mathbb B^n $

Disk

$ \mathbb B^2 $

Ball

$ \mathbb B^3 $

Gongol

$ \mathbb B^4 $

Pentorb

$ \mathbb B^5 $

Hexorb

$ \mathbb B^6 $

Heptorb

$ \mathbb B^7 $

Octorb

$ \mathbb B^8 $

Enneorb

$ \mathbb B^9 $

Dekorb

$ \mathbb B^{10} $

Hendekorb

$ \mathbb B^{11} $

Dodekorb

$ \mathbb B^{12} $

Tridekorb

$ \mathbb B^{13} $

Tetradekorb

$ \mathbb B^{14} $

Pentadekorb

$ \mathbb B^{15} $

Hexadekorb

$ \mathbb B^{16} $

... Omegaball

$ \mathbb B^{\aleph_0} $

$ \{\} $ $ _3\{\} $ $ _4\{\} $ $ _5\{\} $ $ _6\{\} $
Line segment Tricomtelon Tetracomtelon Pentacomtelon Hexacomtelon
Zeroth First Second Third Fourth Fifth
Cosmotopes Point Line segment Pentagon Dodecahedron Hecatonicosachoron Order-3 hecatonicosachoric honeycomb
Hydrotopes Point Line segment Pentagon Icosahedron Hexacosichoron Order-5 pentachoric honeycomb
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