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<head><title>verticesDualPolytope -- The dual vertices of a polytope.</title>
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<div><h1>verticesDualPolytope -- The dual vertices of a polytope.</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>verticesDualPolytope(C)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>an <a href="___Complex.html">embedded complex</a></span>, a polytope</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p>Computes the vertices of the dual polytope of C in the row of a matrix. The rows are sorted according to the <a href="_polytopal__Facets.html" title="The facets of a polytope.">polytopalFacets</a> of C.</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>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</pre>
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<tr><td><pre>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</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_dual__Grading.html" title="The dual vertices of a polytope.">dualGrading</a> -- The dual vertices of a polytope.</span></li>
<li><span><a href="_grading.html" title="The grading of a first order deformation or complex or polynomial ring.">grading</a> -- The grading of a first order deformation or complex or polynomial ring.</span></li>
<li><span><a href="_polytopal__Facets.html" title="The facets of a polytope.">polytopalFacets</a> -- The facets of a polytope.</span></li>
<li><span><a href="_dualize.html" title="The dual of a face or complex.">dualize</a> -- The dual of a face or complex.</span></li>
<li><span><a href="_is__Polytope.html" title="Check whether a complex is a polytope.">isPolytope</a> -- Check whether a complex is a polytope.</span></li>
<li><span><a href="_facets.html" title="The maximal faces of a complex.">facets</a> -- The maximal faces of a complex.</span></li>
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<div class="waystouse"><h2>Ways to use <tt>verticesDualPolytope</tt> :</h2>
<ul><li>verticesDualPolytope(Complex)</li>
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