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verticesDualPolytope -- The dual vertices of a polytope.

Synopsis

Description

Computes the vertices of the dual polytope of C in the row of a matrix. The rows are sorted according to the polytopalFacets of C.

i1 : R=QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing
i2 : C=simplex(R)

o2 = 4: x x x x x  
         0 1 2 3 4

o2 : complex of dim 4 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0
i3 : verticesDualPolytope C

o3 = | -1 -1 -1 4  |
     | -1 -1 4  -1 |
     | -1 4  -1 -1 |
     | 4  -1 -1 -1 |
     | -1 -1 -1 -1 |

              5        4
o3 : Matrix QQ  <--- QQ

See also

  • dualGrading -- The dual vertices of a polytope.
  • grading -- The grading of a first order deformation or complex or polynomial ring.
  • polytopalFacets -- The facets of a polytope.
  • dualize -- The dual of a face or complex.
  • isPolytope -- Check whether a complex is a polytope.
  • facets -- The maximal faces of a complex.

Ways to use verticesDualPolytope :

  • verticesDualPolytope(Complex)