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Improve face generator of polyhedra by exposing FaceIterator class #29654

@kliem

Description

@kliem

Currently, the face generator of polyhedra is a wrapper of the FaceIterator class, which is intended for combinatorial polyhedra.

However, it takes only little effort to modify this to return a PolyhedronFace instead of a CombinatorialFace on next. The class FaceIterator has the advantage that it exposes extra features of FaceIterator. Currently, there is only the possibility of ignoring sub- or supfaces, but there might be more features added later.

It also simplifies it a lot for the user to obtain a PolyhedronFace from FaceIterator as the needed function is not exactly easy to find.

Follow up:

  • Use FaceIterator to obtain the meet of (some) vertices or the join of (some) facets.

This is motivated by https://ask.sagemath.org/question/34485/what-is-the-most-efficient-way-to-look-up-a-face-in-the-face-lattice-of-a-polyhedron/#50965

Depends on #28894

CC: @jplab @LaisRast @videlec

Component: geometry

Keywords: polyhedra, face iterator

Author: Jonathan Kliem

Branch/Commit: 3ba34fd

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/29654

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