#15240: Switch lattice polytopes to point collections
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       Reporter:  novoselt           |        Owner:
           Type:  enhancement        |       Status:  new
       Priority:  major              |    Milestone:  sage-6.0
      Component:  geometry           |   Resolution:
       Keywords:  toric sd53         |    Merged in:
        Authors:  Andrey             |    Reviewers:
  Novoseltsev                        |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:  u/novoselt/lp2pc   |  9e2512e40f2f3428b63e7dc46170a207bcf36ccc
   Dependencies:                     |     Stopgaps:
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Comment (by vbraun):

 Replying to [comment:4 novoselt]:
 > Hey Volker - I think it would be nice to deprecate in this ticket
 everything that we don't want to keep except for the way how faces are
 handled (which I'd rather do in a follow up ticket).

 Sounds good!

 > What about "desc"? I'd like to print polytopes similar to cones/fans:
 "3-d lattice polytope in 4-d lattice N", perhaps with "lattice" replaced
 by "reflexive" automatically and with the index for 2- and 3-d cases.
 Should then "desc" be gone and those who really want can use Sage standard
 "rename"?

 +1

 > Also, I am not sure what the output of "normal_form" should be - keeping
 it as a matrix does not seem a good choice.

 A matrix isn't totally strange, after all the normal form is a version of
 hermite normal form together with permutation of vertices.

 If you want to return it as another `LatticePolytope` then the constructor
 should keep the vertices in the specified order. The ambient lattice
 should be the same as the lattice of the original polytope, imho.

 > `projective_space` and `octahedron(2)` better disappear as well, not
 sure how did I come up with "octa" for vertices other than 8!

 Should probably be `cross_polytope` ;-)

--
Ticket URL: <http://trac.sagemath.org/ticket/15240#comment:6>
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