Opened 7 months ago

Last modified 4 months ago

## #31803 new enhancement

# Make CombinatorialPolyhedron an element class — at Initial Version

Reported by: | mkoeppe | Owned by: | |
---|---|---|---|

Priority: | major | Milestone: | sage-9.5 |

Component: | geometry | Keywords: | |

Cc: | gh-kliem, jipilab, tscrim, jhpalmieri, yzh | Merged in: | |

Authors: | Reviewers: | ||

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

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

... of a parent class `CombinatorialPolyhedra`

in a new category of `CombinatorialPolyhedralSets`

. A parent is defined by (possibly infinite) sets of allowed vertices and facets; every element's set of vertices and facets is a subset of these.

Morphisms in the category are degenerations.

This setup of element/parent/category is parallel to geometric polyhedra: `Polyhedron`

/`Polyhedra`

/`PolyhedralSets`

.

Assigning coordinates in `QQ^3`

to labeled `vertices`

then defines a morphism from `CombinatorialPolyhedra(vertices, facets)`

to `Polyhedra(QQ, 3)`

.

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