> restart:  with(plots):with(plottools):
> A:=([   0,  1,  0]) :
> A1:=([ 0.817, 0.470,  0.329]) :
> A2:=([   1,  0, sqrt(2)]) :
> A3:=([   1,  0,-1 -sqrt(2)/2]) :
> 
> B:=([   -1, 0,  0]) :
> B1:=([ -0.817, 0.470,  -0.329]):
> B2:=([   0,  1,   -sqrt(2)]) :
> B3:=([   -1, 0, -1  -sqrt(2) -sqrt(2)/2]) :
> 
> C:=([   0, -1, 0]) :
> C1:=([ -0.329, -0.470,  0.817]) :  
> C2:=([   -1, 0, sqrt(2)]) :
> 
> C3:=([   -1, 0, -1 -sqrt(2)/2]) :
> X:=([   1, 0,  0]) :
> X1:=([ 0.329, -0.470,  -0.817]) :
> X2:=([   0,  -1,  -sqrt(2) ]) :
> 
> X3:=([   1, 0,  -1  -sqrt(2) -sqrt(2)/2]) :
> E:=([  0,  0, sqrt(2)/2]) :  
> F:=([  0,  0, -sqrt(2)/2]) :  
> E3:=([  0,  0, -1 -sqrt(2)]) :  
> F3:=([  0,  0, -1-2*sqrt(2)]) :  
> 
> P0:=polygonplot3d([[A,E,X],[B,F,A],[E,B,C],[C,F,X],     
>  [A,E,F],[C,E,F],[B,E,F],[X,E,F]]):
> P1:=polygonplot3d([[A1,E,X],[B1,F,A],[E,B,C1],[C,F,X1],     
>  [A,E,F],[C,E,F],[B,E,F],[X,E,F]]):
> P2:=polygonplot3d([[A2,E,X],[B2,F,A],[E,B,C2],[C,F,X2],     
>  [A,E,F],[C,E,F],[B,E,F],[X,E,F]]):
> 
> P3:=polygonplot3d([[A,E,C,F],[F,C, X2],[A,F,B2],
>                    [E3,X3,F3,B3],[A3,X3,E3],[E3,B3,C3]]):
> P4:=polygonplot3d([[A,E,X],[B,F,A],[E,B,C],[C,F,X],     
>  [A,E,F],[C,E,F],[B,E,F],[X,E,F],[A,C,X],[B,A,X]]):
> 
> display(P0,style = patch,scaling=CONSTRAINED,color=BLUE,orientation=[47,73]);

> display(P1,style = patch,scaling=CONSTRAINED,color=RED,orientation=[47,73]);

> display(P2,style = patch,scaling=CONSTRAINED,color=YELLOW,orientation=[47,73]);

> display(P3,style = patch,scaling=CONSTRAINED,color=CYAN,orientation=[47,73]);

> display(P4,style = patch,scaling=CONSTRAINED,color=ORANGE,orientation=[47,73]);

>