gap&gt; ps := HyperbolicQuadric(7,5^3);
Q+(7, 125)
gap&gt; gh := TwistedTrialityHexagon(ps);
T(125, 5) in Q+(7, 125)
gap&gt; repeat
&gt; p := Random(Points(ps));
&gt; until p in gh;
gap&gt; time;
18399
gap&gt; p in gh;
true
gap&gt; q := ElementToElement(gh,p);
&lt;a point in T(125, 5) in Q+(7, 125)&gt;
gap&gt; l := Random(Lines(p));
&lt;a line in Q+(7, 125)&gt;
gap&gt; l in gh;
false
gap&gt; List(Lines(q),x-&gt;x in gh);
[ true, true, true, true, true, true ]
