How to reproduce the following stereometry problem with pst-solides3d?

Question

I am interested in reproducing the following diagram with PSTricks' 3D package named pst-solides3d. Unfortunately I am not familiar with the package and I am not sure whether or not it supports

• translation
• intersection

Could you show me how to reproduce the following with pst-solides3d?

^{I am a sort of person who can't be bothered to read documentation even after wrong things have happened. This is my learning style.}

\documentclass[pstricks,12pt]{standalone}
\usepackage{pst-eucl}
% P on BCGF
% Q on ADHE
% Draw the intersection point S between PQ and BCHE
\begin{document}
\begin{pspicture}showgrid=false(10.5,11)
    % A cube
    \pstGeonodePosAngle={180,0,-60,180}{A}(6,0){B}(9,3){C}(3,3){D}(0,6){E}
    \pstTranslation[PosAngle={0,-45,180}]{A}{E}{B,C,D}[F,G,H]
    \psline(E)(H)(G)(C)(B)(F)(E)(A)(B)
    \psline(F)(G)
    \pslinelinestyle=dashed(D)(C)
    \pslinelinestyle=dashed(D)
% P and Q
\pstGeonode[PosAngle={0,180}](9.5,2){P}(1,9.5){Q}


% Hidden Qt by translating Q along HQ
\pstTranslation[PointName=none,PointSymbol=none]{H}{D}{Q}[Qt]
% Hidden Pt by translating P along CG
\pstTranslation[PointName=none,PointSymbol=none]{C}{G}{P}[Pt]


% Q' = intersection QQt and EH
\pstInterLL[PosAngle=180]{Q}{Qt}{E}{H}{Q'}
% Q'' = intersection QQt and AD
\pstInterLL[PosAngle=160]{Q}{Qt}{A}{D}{Q''}

% P' = intersection PPt and FG
\pstInterLL[PosAngle=0]{P}{Pt}{F}{G}{P'}
% P'' = intersection PPt and BC
\pstInterLL[PosAngle=0]{P}{Pt}{B}{C}{P''}



% auxiliary lines
    \pclinelinecolor=lightgray,nodesepB=-1(P')
    \pclinelinecolor=lightgray,nodesepB=-1(P'')
    \pclinelinecolor=lightgray,nodesep=-1(P)
\pcline[linecolor=lightgray,nodesepB=-1](Q')(Q)
\pcline[linecolor=lightgray,nodesepB=-1,linestyle=dashed](Q')(Q'')


% plane BCHE
\pspolygon[linestyle=none,fillstyle=solid,fillcolor=yellow,opacity=0.2](B)(C)(H)(E)
% plane Q'Q''P''P'
\pspolygon[linestyle=none,fillstyle=solid,fillcolor=green,opacity=0.2](Q')(Q'')(P'')(P')


% common line between two planes
\psline[linecolor=red,linestyle=dashed](Q')(P'')    

% PQ
\psline[linecolor=blue,linestyle=dashed](P)(Q)

% intersection point between PQ and the common line
\pstInterLL[PosAngle=45]{P}{Q}{Q'}{P''}{S}

\end{pspicture}
\end{document}