(Redirected from 1-hypercube)
Rank1
TypeRegular
SpaceSpherical
Info
Coxeter diagramx
Schläfli symbol{}
Tapertopic notation1
Toratopic notationI
Bracket notationI
SymmetryA1, order 2
Elements
Vertex figurePoint
Vertices2
Measures (edge length 1)
Circumradius${\displaystyle \frac12 = 0.5}$
Length1
Central density1
Euler characteristic2
Number of pieces2
Level of complexity1
Related polytopes
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.

It is the one-dimensional simplex, the one-dimensional hypercube, and the one-dimensional orthoplex. It is also the one-dimensional omnitruncated simplex, along with the 1D version of just about any series of general polytopes.

Identical dyads can tile 1d space in the regular apeirogon.

Vertex coordinates

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

• (±1/2).

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.