<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>polytope -- returns a polytope of which the fan is the normal fan if it is polytopal</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_pos__Hull.html">next</a> | <a href="___Polyhedron_sp_eq_eq_sp__Polyhedron.html">previous</a> | <a href="_pos__Hull.html">forward</a> | <a href="___Polyhedron_sp_eq_eq_sp__Polyhedron.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>polytope -- returns a polytope of which the fan is the normal fan if it is polytopal</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> P = polytope F</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<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>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><p/>
If the fan <tt>F</tt> is polytopal then <tt>polytope</tt> returns a polytope <tt>P</tt>. <tt>F</tt> is the
normal fan of this polytope. Note that such a polytope is not unique.<table class="examples"><tr><td><pre>i1 : F = fan {posHull matrix {{1,0},{0,1}},posHull matrix {{0,-1},{1,1}},posHull matrix {{-1,-1},{0,1}},posHull matrix {{-1,1},{0,-1}},posHull matrix {{1,1},{0,-1}}}
o1 = {ambient dimension => 2 }
number of generating cones => 5
number of rays => 5
top dimension of the cones => 2
o1 : Fan</pre>
</td></tr>
<tr><td><pre>i2 : P = polytope F
o2 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 5
number of rays => 0
number of vertices => 5
o2 : Polyhedron</pre>
</td></tr>
</table>
</div>
</div>
<div class="waystouse"><h2>Ways to use <tt>polytope</tt> :</h2>
<ul><li>polytope(Fan)</li>
</ul>
</div>
</div>
</body>
</html>
