\documentclass[border=2mm,12pt,tikz]{standalone}

\usepackage{tikz-3dplot} 

\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools

\pgfdeclarelayer{background} 

\pgfdeclarelayer{foreground}

\pgfdeclarelayer{behind}  

\pgfsetlayers{behind,background,main,foreground}

\begin{document}

\foreach \Angle in {5,15,...,355}

{\tdplotsetmaincoords{60}{\Angle}

\begin{tikzpicture}[tdplot_main_coords,scale=1,line join=round, 

    line cap=round,rounded corners=0.6pt,

    declare function={a=4;b=a/2;}]

 \path[tdplot_screen_coords,use as bounding box] 

    (-1.2*a,-1.2*a) rectangle (1.2*a,1.2*a);

 \path (b,0,-a)  coordinate (A)

  (0,b,-a)  coordinate (B)

  (-b,0,-a) coordinate (C)

  (0,-b,-a) coordinate (D)

  (b,a,0)  coordinate (I)

  (0,a,-b) coordinate (J)

  (-b,a,0)  coordinate (K)

  (0,a,b) coordinate (L)

  (a,-b,0)  coordinate (P)

  (a,0,-b) coordinate (Q)

  (a,b,0)  coordinate (R)

  (a,0,b) coordinate (S)

  [3d coordinate={(A')=(A)+ (0,0,2*a)}, 

   3d coordinate={(B')=(B)+ (0,0,2*a)},  

   3d coordinate={(C')=(C)+ (0,0,2*a)}, 

   3d coordinate={(D')=(D)+ (0,0,2*a)},

%

   3d coordinate={(I')=(I)+ (0,-2*a,0)}, 

   3d coordinate={(J')=(J)+ (0,-2*a,0)},  

   3d coordinate={(K')=(K)+ (0,-2*a,0)}, 

   3d coordinate={(L')=(L)+ (0,-2*a,0)},

%

   3d coordinate={(P')=(P)+ (-2*a,0,0)},

   3d coordinate={(Q')=(Q)+ (-2*a,0,0)},

   3d coordinate={(R')=(R)+ (-2*a,0,0)},

   3d coordinate={(S')=(S)+ (-2*a,0,0)}];

 \tikzset{3d/polyhedron/.cd,fore layer=foreground,back layer=background,

    fore/.style={draw,fill=none,ultra thick,solid},

    back/.style={draw,fill=none,dashed,thin},

    draw face with corners={{(A)},{(B)},{(J)},{(I)},{(R)},{(Q)}},

    draw face with corners={{(I)},{(J)},{(K)},{(L)}},

    draw face with corners={{(K)},{(L)},{(B')},{(C')},{(S')},{(R')}},

    draw face with corners={{(A')},{(B')},{(C')},{(D')}},

    draw face with corners={{(P)},{(Q)},{(R)},{(S)}},

    draw face with corners={{(S)},{(P)},{(I')},{(L')},{(D')},{(A')}},

    draw face with corners={{(I)},{(R)},{(S)},{(A')},{(B')},{(L)}},

    draw face with corners={{(C')},{(D')},{(L')},{(K')},{(P')},{(S')}},

    draw face with corners={{(B)},{(C)},{(Q')},{(R')},{(K)},{(J)}},

    draw face with corners={{(A)},{(D)},{(J')},{(I')},{(P)},{(Q)}},

    draw face with corners={{(A)},{(D)},{(C)},{(B)}},

    draw face with corners={{(C)},{(Q')},{(P')},{(K')},{(J')},{(D)}},

    draw face with corners={ {(L')},{(K')},{(J')},{(I')}},

    draw face with corners={{(R')},{(Q')},{(P')},{(S')}}}

% \foreach \point/\position in {A/below,B/below,C/below,D/left,I/below,J/below,K/right,L/above,P/right,Q/above,R/left,S/below,I'/below,J'/below,K'/right,L'/above,P'/right,Q'/above,R'/left,S'/below,A'/below,B'/below,C'/below,D'/left}

% {\fill (\point) circle (0.0pt);

%   \node[\position=2pt] at (\point) {$\point$};

% }

​

\end{tikzpicture}}

\end{document}