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<p class=MsoNormal><font size=2 face="Times New Roman"><span lang=EN-US
style='font-size:10.5pt'>I want to judge whether a polyhedron is convex or
non-convex by an algorithm. The algorithm is : if every vertex of the
polyhedron is convex then the polyhedron is convex.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face="Times New Roman"><span lang=EN-US
style='font-size:10.5pt'>For each vertex, there is at least three vertexes is
adjacent to it. These vertexes make up of a triangle which forms a plane.
Because the direction of the plane can be gotten by the order of three vertexes
according to right-hand-rule, the order of three vertexes must be counter-clockwise.
If the vertex is above the plane, the vertex is convex. If not, the
vertex is non-convex.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face="Times New Roman"><span lang=EN-US
style='font-size:10.5pt'>But I cannot assure the order of three vertexes is
counter-clockwise.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face="Times New Roman"><span lang=EN-US
style='font-size:10.5pt'>And have you a better way to the question?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face="Times New Roman"><span lang=EN-US
style='font-size:10.5pt'>Look forward to your reply again.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=1 face=Arial><span lang=EN-US style='font-size:
9.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
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