Dyad

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Dyad
Line segment.svg
Rank1
TypeRegular
SpaceSpherical
Bowers style acronymDyad
Info
Coxeter diagramx
Schläfli symbol{}
Tapertopic notation1
Toratopic notationI
Bracket notationI
SymmetryA1, order 2
ArmyDyad
Elements
Vertex figurePoint
Vertices2
Measures (edge length 1)
Circumradius
Length1
Central density1
Euler characteristic2
Number of pieces2
Level of complexity1
Related polytopes
DualDyad
ConjugateDyad
Properties
ConvexYes
OrientableYes
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, and tegum of the point.

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:

  • (±1/2).

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]

  • Hi.gher.Space Wiki Contributors. "Digon".