I was able to solve the problem on my own... Puh!
The Solution is quite simple:
1. Run Polymake with:
polymake 'my $VD = new VoronoiDiagram(SITES=>[[1,1,1],[1,0,1],[1,-1,1],[1,1,-1],[1,0,-1],[1,-1,-1]]);$VD->DUAL_GRAPH->ADJACENCY;save($VD,"OUTPUT.xml");'
2. Eval the output file
The Memory dump in the save file saved my!
I am pretty sure, this was not the last time for calling for help desperatly
Thanks and bye
Timo
p.s. the docu is quite hard for non-mathematicians