The number of combinatorial types of regular projections of a polytope is finite.
I want to find m_j(P), the maximum number of j-faces of a regular projection of P.
Can I do this with polymake? For instance, I am examining the rhombic triacontahedron. By using
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$RTP = projection($RT,[1,2]);
I built an arbitrary rotation matrix $m and did
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$rotRT = transform($RT,$m);
$RTP = projection($rotRT,[2,3]);
How can I know if I've gotten the maximum? Is there a choice of rotations which will give me all the combinatorial types of regular projections? Any hints would be appreciated.