## Lectures on Polytopes |

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### Contents

Preface | 1 |

Polytopes Polyhedra and Cones | 27 |

Faces of Polytopes | 51 |

Copyright | |

9 other sections not shown

### Common terms and phrases

affine arrangement associated assume basic boundary called circuits combinatorially equivalent complex compute condition cone configuration conjecture connected consider construction contained coordinates corresponding cube cyclic d-polytope define Definition deleting denote derive describe determined dimension drawing dual edges element equality example Exercise exists f-vector face facets fact fiber figure finite Gale diagram geometric given graph hyperplane inequalities interior intersection lattice least lecture Lemma linear function maximal minimal Minkowski sum multiset Note obtained oriented matroid particular path plane polar polyhedra polytope poset positive problem projection proof properties prove realization refer regular represented respect result satisfies Schlegel diagram Sect shellable shelling Show sign vectors Similarly simple simplex simplicial simplicial complex space subdivision theorem theory transformation triangulation unique upper bound valid vertex vertices yields zonotope