#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   |  00a1a86f935993a6d3891a570cb16dc53d57cc8f
   Dependencies:                     |     Stopgaps:
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Comment (by 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). So far I've
 deprecated constructing polytopes from matrices, perhaps constructing them
 from files should be deprecated as well and handled by separate functions?

 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"?

 Also, I am not sure what the output of "normal_form" should be - keeping
 it as a matrix does not seem a good choice. Maybe the corresponding
 polytope in `ToricLattice(dim).dual()`? Then polytopes from built-in lists
 will return themselves and be equal to their normal form.

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

--
Ticket URL: <http://trac.sagemath.org/ticket/15240#comment:4>
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