# pure simplicial complex

A finite simplicial complex^{} is *pure* if each facet has the same dimension^{}.

For example, any polytope is pure, but the simplicial complex

$$\{\mathrm{\varnothing},a,b,c,d,ab,ac,bc,cd,abc\}$$ |

is not pure because $cd$ and $abc$ are facets with different dimensions.

Title | pure simplicial complex |
---|---|

Canonical name | PureSimplicialComplex |

Date of creation | 2013-03-22 14:18:52 |

Last modified on | 2013-03-22 14:18:52 |

Owner | mps (409) |

Last modified by | mps (409) |

Numerical id | 5 |

Author | mps (409) |

Entry type | Definition |

Classification | msc 55U10 |

Classification | msc 52B99 |