Dyad

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Dyad
Rank1
TypeRegular
Notation
Bowers style acronymDyad
Coxeter diagramx ()
Schläfli symbol{}
Tapertopic notation1
Toratopic notationI
Bracket notationI
Elements
Vertices2
Vertex figurePoint
Measures (edge length 1)
Circumradius
Length1
Central density1
Number of external pieces2
Level of complexity1
Related polytopes
ArmyDyad
DualDyad
κ ?Dyad
ConjugateNone
Abstract & topological properties
Flag count2
Euler characteristic2
OrientableYes
Properties
SymmetryA1, order 2
Flag orbits1
ConvexYes
NatureTame

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.

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]