11-12 Describe how six identical pipes are joined together symmetrically .

> restart:

> with(plottools):with(plots):

Warning, the name changecoords has been redefined

> x:=cos(t):

> y:=sin(t):

> u:=x:

> z:=(1-s)*2+s*u:

> a1:=plot3d([x,y,z],t=-Pi/4..Pi/4,s=0..1,scaling=constrained,grid=[30,8]):

> a2:=rotate(a1,0,0,2*Pi/4):

> a3:=rotate(a1,0,0,Pi):

> a4:=rotate(a1,0,0,6*Pi/4):

> a:=display(a1,a2,a3,a4):

> b1:=reflect(a,[[0,0,0],[1,0,1],[1,1,1]]):

> b2:=rotate(b1,0,0,2*Pi/4):

> b3:=rotate(b1,0,0,Pi):

> c:=display(a,b1,b2,b3):

> cc:=reflect(c,[0,0,0]):

> p:=display(c,cc):

> p;

> vrml(p,"c:/Program Files/Maple 6/beauty/11-12.wrl",background_color=white);

12-13 . Describe how 12 identical pipes are joined together symmetrically