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