11-4.Describe how three pipes are symmetrically joined.

> restart;

> with(plots):with(plottools):

Warning, the name changecoords has been redefined

> x:=cos(t):

> y:=sin(t):

> u:=x/sqrt(3):

> z:=(1-s)*u+s*(-1.5):

> a:=plot3d([x,y,z],s=0..1,t=Pi/2..3*Pi/2,scaling=constrained,grid=[5,50]):

> b:=plot3d([-x,y,z],s=0..1,t=Pi/2..3*Pi/2,scaling=constrained,grid=[5,50]):

> x1:=cos(2*Pi/3)*x-sin(2*Pi/3)*z:

> z1:=sin(2*Pi/3)*x+cos(2*Pi/3)*z:

> a:=plot3d([x,y,z],s=0..1,t=Pi/2..3*Pi/2,scaling=constrained,grid=[5,50]):

> a1:=plot3d([x1,y,z1],s=0..1,t=Pi/2..3*Pi/2,scaling=constrained,grid=[5,50]):

> b1:=plot3d([-x1,y,z1],s=0..1,t=Pi/2..3*Pi/2,scaling=constrained,grid=[5,50]):

> x2:=cos(4*Pi/3)*x-sin(4*Pi/3)*z:

> z2:=sin(4*Pi/3)*x+cos(4*Pi/3)*z:

> a2:=plot3d([x2,y,z2],s=0..1,t=Pi/2..3*Pi/2,scaling=constrained,grid=[5,50]):

> b2:=plot3d([-x2,y,z2],s=0..1,t=Pi/2..3*Pi/2,scaling=constrained,grid=[5,50]):

> p:=display(a,b,a1,b1,a2,b2):

> p;

> vrml(p,"c:/Program Files/Maple 6/beauty/11-4.wrl",background_color=white);

>