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<head><title>normalFan -- computes the normalFan of a polyhedron</title>
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<div><h1>normalFan -- computes the normalFan of a polyhedron</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> F = normalFan P</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>F</tt>, <span>an object of class <a href="___Fan.html" title="the class of all fans">Fan</a></span></span></li>
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<div class="single"><h2>Description</h2>
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The <tt>normalFan</tt> of a <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a> is the fan generated by the
cones <tt>C_v</tt> for all vertices <tt>v</tt> of the <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a>,
where <tt>C_v</tt> is the dual Cone of the positive Hull of <tt>P-v</tt>.
If <tt>P</tt> is compact, i.e. a polytope, then the normalFan is complete.<table class="examples"><tr><td><pre>i1 : P = convexHull matrix{{1,0,0},{0,1,0}}
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 3
number of rays => 0
number of vertices => 3
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : F = normalFan P
o2 = {ambient dimension => 2 }
number of generating cones => 3
number of rays => 3
top dimension of the cones => 2
o2 : Fan</pre>
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<tr><td><pre>i3 : apply(genCones F,rays)
o3 = {| 1 -1 |, | 1 0 |, | -1 0 |}
| 0 -1 | | 0 1 | | -1 1 |
o3 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>normalFan</tt> :</h2>
<ul><li>normalFan(Polyhedron)</li>
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