Dyad

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Dyad
Line segment.svg
Rank1
TypeRegular
SpaceSpherical
Notation
Bowers style acronymDyad
Coxeter diagramx (CDel node 1.png)
Schläfli symbol{}
Tapertopic notation1
Toratopic notationI
Bracket notationI
Elements
Vertices2
Vertex figurePoint
Measures (edge length 1)
Circumradius
Length1
Central density1
Number of pieces2
Level of complexity1
Related polytopes
ArmyDyad
DualDyad
ConjugateNone
Abstract properties
Flag count2
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryA1, order 2
ConvexYes
NatureTame

The dyad,[1] ditelon, dion[2] or simply line segment, is the only possible polytelon. Its facets are two points. It appears as the edges 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[edit | edit source]

Coordinates for the vertices of a line segment of length 1 are simply the points:

Representations[edit | edit source]

The dyad has two distinct representations:

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

References[edit | edit source]

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

External links[edit | edit source]