project an image in a surface in tikzpicture

Question

I've a 3D form like below and I want to project that marker in every surface of that form including the one on the top but not the ones behind.. Anyway, I want just to know the way how projection works and if its possible

\documentclass{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}

% The following code is generated by Sketch. I have edited it a bit
% to make it easier to read.
\begin{tikzpicture}[join=round]
    \tikzstyle{conefill} = [fill=blue!20,fill opacity=0.8]
    \tikzstyle{ann} = [fill=white,font=\footnotesize,inner sep=1pt]
    \tikzstyle{ghostfill} = [fill=white]
         \tikzstyle{ghostdraw} = [draw=black!50]

    % Second version of the cone
    \begin{scope}[xshift=3.5cm]
    \filldraw[ghostdraw,ghostfill](-.775,1.922)--(-1.162,.283)--(-.274,.5)
                                   --(-.183,2.067)--cycle;
    \filldraw[ghostdraw,ghostfill](-.183,2.067)--(-.274,.5)--(.775,.424) 
                                   --(.516,2.016)--cycle;
    \filldraw[ghostdraw,ghostfill](.516,2.016)--(.775,.424)--(1.369,.1)
                                   --(.913,1.8)--cycle;
    \filldraw[ghostdraw,ghostfill](-.913,1.667)--(-1.369,-.1)--(-1.162,.283)
                                   --(-.775,1.922)--cycle;
    \filldraw[ghostdraw,ghostfill](.913,1.8)--(1.369,.1)--(1.162,-.283)
                                   --(.775,1.545)--cycle;
    \filldraw[ghostdraw,ghostfill](-.516,1.45)--(-.775,-.424)--(-1.369,-.1)
                                   --(-.913,1.667)--cycle;
    \filldraw[ghostdraw,ghostfill](.775,1.545)--(1.162,-.283)--(.274,-.5)
                                   --(.183,1.4)--cycle;
    \filldraw[fill=red,fill opacity=0.5](-.516,1.45)--(-.775,-.424)--(.274,-.5)
                                         --(.183,1.4)--cycle;

    \fill(-.775,-.424) circle (2pt);
    \fill(.274,-.5) circle (2pt);
    \fill(-.516,1.45) circle (2pt);
    \fill(.183,1.4) circle (2pt);
    \path[font=\footnotesize]
            (.913,1.8) node[right] {$i\hbox{$=$}0$}
            (1.369,.1) node[right] {$i\hbox{$=$}1$};
    \path[font=\footnotesize]
            (-.645,.513) node[left] {$j$}
            (.228,.45) node[right] {$j\hbox{$+$}1$};
    \fill[black,font=\footnotesize]
                    (-.516,1.45) node [above] {$P_{00}$}
                    (-.775,-.424) node [below] {$P_{10}$}
                    (.183,1.4) node [above] {$P_{01}$}
                    (.274,-.5) node [below] {$P_{11}$};

    \node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[scale=0.1]{download.png}};
    \end{scope}

\end{tikzpicture}


\end{document}

Answer 1

More proof of concept than anything else, but basic idea is to draw the shape over a unit square with the vectors set to 1pt (rather than import it) which can be stretched over the required quadrilateral using a non-linear transform.

Setting up the coordinates is tricky (a lot of trial an error).

\documentclass[tikz,border=5]{standalone}
\usepgfmodule{nonlineartransformations}
\makeatletter
\def\stretchovertransform{%
  \pgfgetlastxy\x\y
  \pgfpointlineattime{\y}
    {\pgfpointlineattime{\x}{\southwest}{\southeast}}%
    {\pgfpointlineattime{\x}{\northwest}{\northeast}}%
}
\tikzset{%
  stretch over/.code args={(#1)#2(#3)#4(#5)#6(#7)}{
    \pgfextract@process\southwest{\tikz@scan@one@point\relax(#1)}%
    \pgfextract@process\northwest{\tikz@scan@one@point\relax(#3)}%
    \pgfextract@process\northeast{\tikz@scan@one@point\relax(#5)}%
    \pgfextract@process\southeast{\tikz@scan@one@point\relax(#7)}%
    \tikzset{reset cm, x=1pt, y=1pt}%
    \pgftransformnonlinear{\stretchovertransform}
  }
}
\tikzstyle{conefill} = [fill=blue!20,fill opacity=0.8]
\tikzstyle{ann} = [fill=white,font=\footnotesize,inner sep=1pt]
\tikzstyle{ghostfill} = [fill=white]
\tikzstyle{ghostdraw} = [draw=black!50]
\begin{document}
\begin{tikzpicture}[line join=round, line cap=round]
\filldraw[ghostdraw, ghostfill](-.775,1.922)--(-1.162,.283)--(-.274,.5)
                               --(-.183,2.067)--cycle;
\filldraw[ghostdraw, ghostfill](-.183,2.067)--(-.274,.5)--(.775,.424) 
                               --(.516,2.016)--cycle;
\filldraw[ghostdraw, ghostfill](.516,2.016)--(.775,.424)--(1.369,.1)
                               --(.913,1.8)--cycle;
\filldraw[ghostdraw, ghostfill](-.913,1.667)--(-1.369,-.1)--(-1.162,.283)
                               --(-.775,1.922)--cycle;
\filldraw[ghostdraw, ghostfill](.913,1.8)--(1.369,.1)--(1.162,-.283)
                               --(.775,1.545)--cycle;
\filldraw[ghostdraw, ghostfill]
  (-.516,1.45) coordinate (r01)  --
  (-.775,-.424) coordinate (r11) --
  (-1.369,-.1) coordinate (r10)  --
  (-.913,1.667) coordinate (r00) -- cycle;
\filldraw[ghostdraw, ghostfill]
  (.775,1.545) coordinate (q01) --
  (1.162,-.283) coordinate (q11) --
  (.274,-.5) coordinate (q10) --
  (.183,1.4) coordinate (q00) -- cycle;
\filldraw[fill=red,fill opacity=0.5]
  (-.516,1.45) coordinate (p00) -- 
  (-.775,-.424) coordinate (p10) --
  (.274,-.5) coordinate (p11) --
  (.183,1.4) coordinate (p01) --cycle;

\foreach \i in {p,q,r}{
  \begin{scope}[stretch over={(\i10) (\i00) (\i01) (\i11)}, shift={(0.5,0.5)}, fill=gray, opacity=.875, scale=0.75]                             
  \fill [even odd rule] 
    (-.5,-.5) rectangle ++(1, 1)  (0,0) 
    circle [radius=0.375]
    (90:.375) -- (210:.375) -- (330:.375)
    (90:.25) -- (210:.25) -- (330:.25); 
  \fill (-.1,-.025) rectangle (.1,.025) 
    [rotate=90](-.1,-.025) rectangle (.1,.025) ;
  \fill [white, shift=(45:.5), scale=0.75] (-.1,-.025) rectangle (.1,.025) 
    [rotate=90](-.1,-.025) rectangle (.1,.025) ;
  \fill [white, shift=(225:.5), scale=0.75] (-.1,-.025) rectangle (.1,.025) 
    [rotate=90](-.1,-.025) rectangle (.1,.025);
  \fill [white, shift=(135:.5), rotate=45] (90:.1) -- (210:.1) -- (330:.1);
  \fill [white, shift=(315:.5), rotate=-135] (90:.1) -- (210:.1) -- (330:.1);
  \end{scope}
}                
\end{tikzpicture}
\end{document}