5.1 3-d plot of a tetrahedron (6.9.00)

5.1.1 John J. Reinmann (23.10.01)

Can anyone show me an efficient way to get a 3-D plot of the tetrahedron formed by the following four points in 3-space:

(1,4,-1), (2,0,0), (-1,-4,3), (4,5,7) ?
 

I would like each surface to have a different color.

5.1.2 Robert Israel (7.9.00)

Sure.

  pts:= [[1,4,-1], [2,0,0], [-1,-4,3], [4,5,7]]; 
  triples:= combinat[choose](pts, 3); 
  colours:= [seq(colour=COLOUR(RGB,op(j)), j=_COLORRGB)]; 
  plots[display](zip(plots[polygonplot3d], triples, colours), 
    scaling=constrained);
 

5.1.3 Carl DeVore (7.9.00)

Here’s a proc to draw any tetrahedron with any four colors.

 DrawTetrahedron:= proc(Pts,Colors) 
    local it,k; 
    it:= combstruct[iterstructs](Combination(Pts), size= 3); 
    RETURN 
       (plots[display] 
          ([seq 
             (plots[display] 
                (PLOT3D(POLYGONS(combstruct[nextstruct](it))) 
                ,color= Colors[k] 
                ) 
             ,k= 1..4 
             ) 
           ], args[3..nargs] 
          ) 
       ) 
 end: 
 
 DrawTetrahedron 
    ([[1,4,-1],[2,0,0],[-1,-4,3],[4,5,7]] 
    ,[red,green,blue,yellow] 
    ,axes= boxed 
    );
 

5.1.4 John S Robinson (8.9.00)

This works:

> with(combinat): 
> vertices:=[[1,4,-1], [2,0,0], [-1,-4,3], [4,5,7]]; 
 
     vertices := [[1, 4, -1], [2, 0, 0], [-1, -4, 3], [4, 5, 7]] 
 
> faces:=choose(vertices,3); 
 
  faces := [[[1, 4, -1], [2, 0, 0], [-1, -4, 3]], 
 
        [[1, 4, -1], [2, 0, 0], [4, 5, 7]], 
 
        [[1, 4, -1], [-1, -4, 3], [4, 5, 7]], 
 
        [[2, 0, 0], [-1, -4, 3], [4, 5, 7]]] 
 
> PLOT3D(POLYGONS(op(faces)));
 

... but it was lucky you wanted a tetrahedron, since all triples of vertices are the faces.

I wish there were some way to plug our own co-ordinates into plotpolyhedra().

5.1.5 Klaus Volpert (12.9.00)

with(plots):with(plottools): 
 a:=[1,4,-1]: 
 b:=[2,0,0]: 
 c:=[-1,-4,3]: 
 d:=[4,5,7]: 
 side1:=polygon([a,b,c],color=green): 
 side2:=polygon([a,b,d],color=red): 
 side3:=polygon([a,c,d],color=blue): 
 side4:=polygon([b,c,d],color=gold): 
 display([side1,side2,side3,side4]);
 

5.1.6 Helmut Kahovec (14.9.00)

You may use gtetrahedron() of the geom3d package:

restart; 
with(geom3d): 
Warning, the name polar has been redefined 
 
point(P1,1,4,-1),point(P2,2,0,0),point(P3,-1,-4,3),point(P4,4,5,7); 
 
                            P1, P2, P3, P4 
 
gtetrahedron(T,[P1,P2,P3,P4]); 
 
                                  T 
 
draw(T,axes=BOXED,scaling=UNCONSTRAINED,labels=[x,y,z]);