#18213: A lot of polytopes constructor are broken
--------------------------+----------------------------
   Reporter:  vdelecroix  |            Owner:
       Type:  defect      |           Status:  new
   Priority:  major       |        Milestone:  sage-6.7
  Component:  geometry    |         Keywords:
  Merged in:              |          Authors:
  Reviewers:              |  Report Upstream:  N/A
Work issues:              |           Branch:
     Commit:              |     Dependencies:
   Stopgaps:              |
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 A lot of polytopes constructors in `sage.geometry.polyhedron.library`.

 1. The Rhombicuboctahedron does not return what it should (as Python
 division was thought as Sage integer divisions). There is in the code
 {{{
 verts = [ [-3/2, -1/2, -1/2], [-3/2, -1/2, 1/2], [-3/2, 1/2, -1/2],
 ...
 }}}

 2. The `great_rhombicuboctahedron` is defined over `QQ` but it should be
 defined over `QQ[sqrt(2)]`!! There are in two places rough approximation
 of sqrt(2) in the code
 {{{
 v1 = QQ(131739771357/54568400000)   # ~ sqrt(2) + 1
 v2 = QQ(104455571357/27284200000)   # ~ 2 sqrt(2)
 }}}
   Now that Sage supports Polyhedron over number fields, we should use
 them!

--
Ticket URL: <http://trac.sagemath.org/ticket/18213>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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