Cfrgtkky

I am new LaTex user and I have hard time plot the following shape in LaTex. I started the shape but I can't find way to finish it if you can help me please

Here is my code

documentclass{article}

usepackage{tikz}       

usepackage{mathrsfs}   

begin{document}

begin{tikzpicture}

    draw (3,0) node {$mathcal{C}$};

    draw (-2,2)--(0,0);

    draw (3,1.5)--(0,0);

    draw (-2,-2)--(0,0);

    draw (3,-1.5)--(0,0);

end{tikzpicture}



end{document}

Here is the shape I am aiming to get if you can help me finish it please.

It is always a bit hard to undo the projection, i.e. to guess the 3d coordinates from their projections on the screen. So most likely I got some wrong, yet this may serve as a start. I recommend using tikz-3dplot because it allows you to do orthographic projections from 3d to the screen. That is, you can adjust the view angles to your needs.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

begin{document}

tdplotsetmaincoords{70}{20}

begin{tikzpicture}[dot/.style={circle,fill,inner sep=1pt}]

  tdplotsetrotatedcoords{30}{20}{0}    

  begin{scope}[tdplot_rotated_coords]

    draw (0,0,0) node[dot,label=left:{$O$}] (O) {} 

        -- (0,0,5) node[pos=1.1] (A) {$A$}; % A=z

    draw (O) -- (4,0,0) node[pos=1.1] (B) {$B$}; % B=x

    draw (O) -- (0,5,0) node[pos=1.1] (C) {$C$}; % C=y

    draw (0,0,1) -- ++ (0,1,0) -- ++ (0,0,-1);

    draw[dotted,thick] (0,0,3) node[dot,label=right:{$widetilde{theta}$}]{} 

        -- (0,5,3) node[dot,label=above:{$X$}]{}; 

    draw (0,0,4)-- ++ (0,1,0) -- ++ (0,0,-1);

    draw (O) -- (0,-3,-3) node[pos=1.1]{$D$}; 

    draw (1,0,0) -- ++ (0,{-1/sqrt(2)},{-1/sqrt(2)}) -- ++ (-1,0,0);

    draw[dotted,thick] (1.5,0,0) node[dot,label=above:{$widetilde{theta}$}]{}

     -- ++ (0,-3,-3) node[dot,label=right:{$X$}]{}; 

    draw (2.5,0,0) -- ++ (0,{-1/sqrt(2)},{-1/sqrt(2)}) -- ++ (-1,0,0);

    path (B) -- (A) node[pos=0.3]{$mathcal{C}$};

    draw[dotted,thick] (O) -- (0,3,-3) node[dot,label=left:{$X$}]{};

  end{scope}

  begin{scope}[xshift=7cm,tdplot_rotated_coords]

    draw (0,0,0) node[dot,label=left:{$O$}] (O) {} 

        -- (0,0,5) node[pos=1.1] (A) {$A$}; % A=z

    draw (O) -- (4,0,0) node[pos=1.1] (B) {$B$}; % B=x

    draw (O) -- (0,5,0) node[pos=1.1] (C) {$C$}; % C=y

    draw (0,0,1) -- ++ (0,1,0) -- ++ (0,0,-1);

    draw (0,0,3) node[dot,label=right:{$Q$}] (Q) {} 

        -- (0,5,3) node[dot,label=above:{$P$}]{}; 

    draw (0,0,4)-- ++ (0,1,0) -- ++ (0,0,-1);

    draw (O) -- (0,-3,-3) node[pos=1.1]{$D$}; 

    draw (1,0,0) -- ++ (0,{-1/sqrt(2)},{-1/sqrt(2)}) -- ++ (-1,0,0);

    draw (1.5,0,0) node[dot,label=above right:{$R$}] (R) {}

     -- ++ (0,-3,-3) node[dot,label=right:{$S$}]{}; 

    draw (2.5,0,0) -- ++ (0,{-1/sqrt(2)},{-1/sqrt(2)}) -- ++ (-1,0,0);

    path (B) -- (A) node[pos=0.3]{$mathcal{C}$};

    draw (R) to[out=80,in=-40] (Q);

  end{scope}

end{tikzpicture}

end{document}