# Ray

Ray | |
---|---|

Rank | 1 |

Type | Regular |

Notation | |

Bowers style acronym | Ray |

Elements | |

Vertices | 1 |

Vertex figure | Point |

Measures | |

Length | |

Central density | 1 |

Related polytopes | |

Dual | Ray |

Abstract & topological properties | |

Flag count | 1 |

Euler characteristic | 1 |

Surface | Point |

Orientable | Yes |

Properties | |

Symmetry | I, order 1 |

Convex | Yes |

Nature | Tame |

The **ray** is a geometric object consisting of a point and a line extending indefinitely in one direction. Although it shares many properties with polytopes it is generally not considered a polytope.

## Abstract[edit | edit source]

The elements of a ray form a ranked and bounded poset, however they do not meet the diamond property and thus the ray is not an abstract polytope. Polytopoids that fail the diamond property are often called exotic, so the ray can be thought of as an exotic 1-polytope. It is the smallest possible rank 1 poset.

While it itself is not a polytope, a compound of two rays is abstractly a dyad, making it the only ranked and bounded poset that has a non-trivial compound which is an abstract polytope. The dyad does not meet the definition for a compound and thus, rather paradoxically, compounds of rays are not considered compounds. Geometrically a compound of two rays is an antidyad.

## See also[edit | edit source]

## External links[edit | edit source]

- Wikipedia contributors. "Ray (geometry)".
- Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".

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