# Point

The **point** (also called **monad** or **monon**^{[1]}). is the only possible 0-polytope or polyon. If the nullitope is not considered, this is the simplest possible polytope overall, as it has no other lower-dimensional elements. It appears as the vertices in all higher polytopes.

Point | |
---|---|

Rank | 0 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Point |

Coxeter diagram | |

Elements | |

Vertex figure | Nullitope |

Measures (edge length 1) | |

Central density | 1 |

Number of external pieces | 1 |

Level of complexity | 1 |

Related polytopes | |

Army | Point |

Dual | Point |

Conjugate | None |

Abstract & topological properties | |

Flag count | 1 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{0}, order 1 |

Convex | Yes |

Nature | Tame |

A point is simultaneously a 0-simplex, a 0-hypercube, and a 0-orthoplex. Furthermore, a point is the pyramid of the nullitope.

Somewhat contrary to intuition, the point is technically asymmetrical, as its only automorphism is trivial.

## Vertex coordinatesEdit

Coordinates for a point are simply:

- .

## ReferencesEdit

- ↑ Inchbald, Guy. http://www.steelpillow.com/polyhedra/ditela.html

## External linksEdit

- Bowers, Jonathan. "Zero Dimensional Shapes".

- Wikipedia Contributors. "Point (geometry)".