Implement one-point suspension and face split of polyhedron

[jplab]

The one-point suspension of a vertex v of a polyhedron P of dimension d is obtained by placing P in a dimension d+1 vector space where the last coordinate is 0, then placing a vertex "over" v and a vertex "below" v in the last coordinate and taking the convex hull.

One can do a similar construction for faces of polyhedron by placing the two vertices relative to the center of the face. This way we get the face split of P.

On the way, the center function also got modified in the case when it is only a vertex so that it returns the vertex. This was necessary to make the one-point suspension consistent.

CC: @videlec @mo271 @mkoeppe @fchapoton

Component: geometry

Keywords: days93, polytope, thursdaysbdx, IMA-PolyGeom

Author: Jean-Philippe Labbé

Branch/Commit: 2d78b87

Reviewer: Frédéric Chapoton, Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/24886

[jplab]

Branch: u/jipilab/24886

[jplab]

New commits:

32f0e86	first version of ops
eeee559	Second version of ops
2dacbe1	whitespaces

[jplab]

Commit: 2dacbe1

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

02fa0d9

Merge branch 'sage8.2.b7' into onepointsus

[sagetrac-git]

Changed commit from 2dacbe1 to 02fa0d9

[videlec]

comment:4

typo: the face splitting the face ``face``

[videlec]

comment:5

You should check that you obtain the same answer using a proper vertex or a face of dimension 0

sage: C = polytopes.cube()
sage: C.faces(0)    # dimension 0 faces
(<0>, <1>, <2>, <3>, <4>, <5>, <6>, <7>)
sage: C.vertices()  # proper vertices
(A vertex at (-1, -1, -1),
 A vertex at (-1, -1, 1),
...
 A vertex at (1, 1, 1))

[videlec]

comment:6

The documentation would also be nicer with:

• a proper definition of bypiramid
• specification that the newly added vertices will be at height -1 and 1

[videlec]

Changed keywords from days93, polytope to days93, polytope, thursdaysbdx

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

7f5e125	fixed typos in polyhedra_quickref.rst
bd6c356	LateX -> LaTeX in polytope_tikz.rst
b1ce45b	Several other corrections
d526f70	renamed tutorial files
d7896f8	Merge branch 'develop' into 22572
597b802	Merge branch sage8.2.rc1 into 22572
eee533a	Corrections from review
b74ae85	Made tests pass
1c9a654	Merge branch thematic tutorial into onepointsus
eef860f	Applied review suggestions

[sagetrac-git]

Changed commit from 02fa0d9 to eef860f

[jplab]

Changed keywords from days93, polytope, thursdaysbdx to days93, polytope, thursdaysbdx, IMA-PolyGeom

[jplab]

comment:9

Hi,

Thanks Vincent for your review. I made the suggested changes (along with merging the tutorial).

I realized while making a test that the method center was changing the base ring when it was taken over a vertex, I fixed that small thing on the way too.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2d78b87

whitespaces

[sagetrac-git]

Changed commit from eef860f to 2d78b87

[fchapoton]

comment:12

ok, let it be too

[fchapoton]

Reviewer: Frédéric Chapoton, Vincent Delecroix

[vbraun]

Changed branch from u/jipilab/24886 to 2d78b87