# Dyad

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.

Dyad | |
---|---|

Rank | 1 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Dyad |

Coxeter diagram | x () |

Schläfli symbol | {} |

Tapertopic notation | 1 |

Toratopic notation | I |

Bracket notation | I |

Elements | |

Vertices | 2 |

Vertex figure | Point |

Measures (edge length 1) | |

Circumradius | |

Length | 1 |

Central density | 1 |

Number of external pieces | 2 |

Level of complexity | 1 |

Related polytopes | |

Army | Dyad |

Dual | Dyad |

Conjugate | None |

Abstract & topological properties | |

Flag count | 2 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{1}, order 2 |

Convex | Yes |

Nature | Tame |

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 coordinatesEdit

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

## RepresentationsEdit

The dyad has two distinct representations:

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

## ReferencesEdit

- ↑ Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".
- ↑ Johnson, Norman W.
*Geometries and transformations*. p. 224.

## External linksEdit

- Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".

- Wikipedia Contributors. "Line segment".
- Hi.gher.Space Wiki Contributors. "Digon".

- Hartley, Michael. "{}*2".