# Element

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An **element** of a polytope *P* is a polytope belonging to *P*. It is ambiguous whether *P* itself counts as an element.

A **pseudoelement** of a polytope *P* is a polytope whose lower-dimensional elements are all elements of *P*, but which is not an element of *P*. For example, the octahedron has three pseudo-squares, while the tetrahemihexahedron (which has the same edges) has the same squares as faces. However, four of the octahedron's faces are pseudo-faces of the tetrahemihexahedron.

## Naming[edit | edit source]

Elements have special names based on their dimensionality.

Rank | Name |
---|---|

0 | Vertex |

1 | Edge |

2 | Face |

3 | Cell |

4 | Teron |

5 | Peton |

6 | Exon |

7 | Zetton |

8 | Yotton |

9 | Xennon |

... | |

n–4 |
Spire |

n–3 |
Peak |

n–2 |
Ridge |

n–1 |
Facet |

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