# Dyad

(Redirected from 1-hypercube)

Jump to navigation
Jump to search
Dyad | |
---|---|

Rank | 1 |

Type | Regular |

Space | Spherical |

Bowers style acronym | Dyad |

Info | |

Coxeter diagram | x |

Schläfli symbol | {} |

Tapertopic notation | 1 |

Toratopic notation | I |

Bracket notation | I |

Symmetry | A1, order 2 |

Army | Dyad |

Elements | |

Vertex figure | Point |

Vertices | 2 |

Measures (edge length 1) | |

Circumradius | |

Length | 1 |

Central density | 1 |

Euler characteristic | 2 |

Number of pieces | 2 |

Level of complexity | 1 |

Related polytopes | |

Dual | Dyad |

Conjugate | Dyad |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

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[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]

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

## External links[edit | edit source]

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

- Wikipedia Contributors. "Line segment".

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