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<head><title>faceFan -- computes the fan generated by the cones over the faces</title>
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<div><h1>faceFan -- computes the fan generated by the cones over the faces</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 = faceFan 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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For a polyhedron with the origin in its relative interior, the face fan is the fan
generated by the cones over the faces of the polytope. Hence the origin must be in hte relative interior.<table class="examples"><tr><td><pre>i1 : P = hypercube 2
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : F = faceFan P
o2 = {ambient dimension => 2 }
number of generating cones => 4
number of rays => 4
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 1 |, | -1 -1 |, | 1 1 |}
| 1 1 | | -1 -1 | | -1 1 | | -1 1 |
o3 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>faceFan</tt> :</h2>
<ul><li>faceFan(Polyhedron)</li>
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