The dyad,[1] ditelon, dion[2] or simply line segment, is the only possible 1-polytope (rarely polytelon). Its facets are two points. It appears as the edges of all higher polytopes.

Rank1
TypeRegular
SpaceSpherical
Notation
Coxeter diagramx ()
Schläfli symbol{}
Tapertopic notation1
Toratopic notationI
Bracket notationI
Elements
Vertices2
Vertex figurePoint
Measures (edge length 1)
Circumradius${\displaystyle \frac12 = 0.5}$
Length1
Central density1
Number of pieces2
Level of complexity1
Related polytopes
ConjugateNone
Abstract properties
Flag count2
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryA1, order 2
ConvexYes
NatureTame

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:

• ${\displaystyle \left(\pm\frac12\right).}$

## Representations

The dyad has two distinct representations:

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

## References

1. Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".
2. Johnson, Norman W. Geometries and transformations. p. 224.