View source for Dyad

{{Infobox polytope
|image=Line segment.svg
|off = Dyad.off
|dim = 1
|type=[[Regular]]
|obsa = Dyad
|vertices = 2
|verf = [[Point]]
|schlafli = {}
|coxeter = x ({{CDD|node_1}})
|army='''Dyad'''
|symmetry = [[Dyadic symmetry|A<sub>1</sub>]], order 2
|smm = Yes
|circum = <math>\frac12 = 0.5</math>
|len=1
|flags = 2
|pieces = 2
|loc = 1
|dual='''Dyad'''
|conjugate=None
|conv = Yes
|orientable = Yes
|nat = Tame
|taper = 1
|tora = <nowiki>I</nowiki>
|bracket = <nowiki>I</nowiki>
}}
The '''dyad''',<ref>{{Bowers|polytela|Regular Polytela and Other One Dimensional Shapes}}</ref> '''ditelon''', '''dion'''<ref>{{cite book|first=Norman W.|last=Johnson|title=Geometries and transformations|pages=224}}</ref> or simply '''line segment''', is the only possible 1-[[polytope]] (rarely ''polytelon''). Its [[facet]]s are two [[point]]s. It appears as the [[edge]]s of all higher polytopes.

A dyad is simultaneously the 1-[[simplex]], the 1-[[hypercube]], and the 1-[[orthoplex]]. Furthermore, a dyad is the [[pyramid]], [[prism]], [[tegum]], [[ditope]], and [[hosotope]] of the [[point]]. It may also be considered a 0-[[hypersphere]].

Congruent dyads can tile 1D space as the regular [[apeirogon]].

==Vertex coordinates==
Coordinates for the vertices of a line segment of length 1 are simply the points:
*<math>\left(\pm\frac12\right).</math>

==Representations==

The dyad has two distinct representations:

*x (full symmetry, vertices are the same)
*oo&#x (vertices considered of different types)

==References==
{{Reflist}}

==External links==
*{{Bowers|polytela|Regular Polytela and Other One Dimensional Shapes}}
*{{Wikipedia|Line segment}}
*{{hgs_wiki|Digon}}
*{{atlas|2/1/1|{}*2}}

{{Simplex}}
{{Hypercube}}
{{Orthoplex}}

[[Category:Simplexes|01-simplex]]
[[Category:Orthoplexes|01-orthoplex]]
[[Category:Hypercubes|01-cube]]
[[Category:1D pyramids]]
[[Category:1D prisms]]
[[Category:1D tegums]]
[[Category:Polytela|2-telon]]
[[Category:A1 symmetry]]
[[Category:Hyperspheres]]