<?xml version="1.0" encoding="UTF-8"?>
<problem xmlns="http://geocentral.net">
<version>3.2</version>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocetral.net/stelian</web>
</author>
<comments>This is a sample Geometria problem.</comments>
</envelope>
<text>Find a path along this figure's edges, which starts at a vertex, ends at the same vertex and visits every vertex exactly once.</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Figure</name>
<color>#ffff</color>
<transparent>true</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>1.0 1.0 1.0</coords>
</point>
<point>
<label>B</label>
<coords>1.0 1.0 -1.0</coords>
</point>
<point>
<label>C</label>
<coords>1.0 -1.0 1.0</coords>
</point>
<point>
<label>E</label>
<coords>-1.0 1.0 1.0</coords>
</point>
<point>
<label>D</label>
<coords>1.0 -1.0 -1.0</coords>
</point>
<point>
<label>F</label>
<coords>-1.0 1.0 -1.0</coords>
</point>
<point>
<label>G</label>
<coords>-1.0 -1.0 1.0</coords>
</point>
<point>
<label>H</label>
<coords>-1.0 -1.0 -1.0</coords>
</point>
<point>
<label>I</label>
<coords>0.0 0.6180339887498949 1.618033988749895</coords>
</point>
<point>
<label>J</label>
<coords>0.0 0.6180339887498949 -1.618033988749895</coords>
</point>
<point>
<label>K</label>
<coords>0.0 -0.6180339887498949 1.618033988749895</coords>
</point>
<point>
<label>L</label>
<coords>0.0 -0.6180339887498949 -1.618033988749895</coords>
</point>
<point>
<label>M</label>
<coords>0.6180339887498949 1.618033988749895 0.0</coords>
</point>
<point>
<label>N</label>
<coords>0.6180339887498949 -1.618033988749895 0.0</coords>
</point>
<point>
<label>O</label>
<coords>-0.6180339887498949 1.618033988749895 0.0</coords>
</point>
<point>
<label>P</label>
<coords>-0.6180339887498949 -1.618033988749895 0.0</coords>
</point>
<point>
<label>Q</label>
<coords>1.618033988749895 0.0 0.6180339887498949</coords>
</point>
<point>
<label>R</label>
<coords>1.618033988749895 0.0 -0.6180339887498949</coords>
</point>
<point>
<label>S</label>
<coords>-1.618033988749895 0.0 0.6180339887498949</coords>
</point>
<point>
<label>T</label>
<coords>-1.618033988749895 0.0 -0.6180339887498949</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.5328608041697043 -0.3348186344436886 -0.4134665796294599 0.6580282918981487</attitude>
</camera>
</figure>
</figures>
<answer>
<type>lineSet</type>
<condition>
<type>hamiltonianCycle</type>
<figureName>Figure</figureName>
</condition>
</answer>
</problem>