Opened 2 years ago

Last modified 2 years ago

## #27973 closed enhancement

# Implement wedge over a face of Polyhedron — at Initial Version

Reported by: | jipilab | Owned by: | |
---|---|---|---|

Priority: | major | Milestone: | sage-8.9 |

Component: | geometry | Keywords: | polytopes, days100, wedge, facet |

Cc: | jipilab, gh-LaisRast, gh-kliem | Merged in: | |

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

From https://www.csun.edu/~ctoth/Handbook/chap15.pdf:

The wedge over a facet `F`

of a polytope `P`

is defined as the product:

`P \times \mathbb{R}\cap \{a^\top x +|x_{d+1} \leq b|\}`

where `F`

is a facet defined by `a^\top x leq b`

.

It has dimension `d+1`

, `m+1`

facets, and `2n-n_F`

vertices, if `F`

has `n_F`

vertices. More generally, the wedge construction can be performed (defined by the same formula) for a face `F`

.

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