# verticesDualPolytope -- The dual vertices of a polytope.

## Synopsis

• Usage:
verticesDualPolytope(C)
• Inputs:
• C, , a polytope
• Outputs:
• ,

## 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

• 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)"

## For the programmer

The object verticesDualPolytope is .