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<head><title>bipyramid -- computes the bipyramid over a polyhedron</title>
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<div><h1>bipyramid -- computes the bipyramid over 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> Q = bipyramid 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>Q</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
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<div class="single"><h2>Description</h2>
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The <tt>bipyramid</tt> over a <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a> in n-space is constructed by
embedding the Polyhedron into (n+1)-space, computing the barycentre of the vertices,
which is a point in the relative interior, and taking the convex hull of the embedded
Polyhedron and the barycentre <tt>x {+/- 1}</tt>.<p/>
As an example, we construct the octahedron as the bipyramid over the square
(see <a href="_hypercube.html" title="computes the d-dimensional hypercube with edge length 2*s">hypercube</a>).<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 : Q = bipyramid P
o2 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 8
number of rays => 0
number of vertices => 6
o2 : Polyhedron</pre>
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<tr><td><pre>i3 : vertices Q
o3 = | -1 1 -1 1 0 0 |
| -1 -1 1 1 0 0 |
| 0 0 0 0 -1 1 |
3 6
o3 : Matrix QQ <--- QQ</pre>
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<div class="waystouse"><h2>Ways to use <tt>bipyramid</tt> :</h2>
<ul><li>bipyramid(Polyhedron)</li>
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