11-13 Describe how 12 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*((sqrt(5)/2)+(1/2)):

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

> a1:=plot3d([x,y,z],t=-Pi/5..Pi/5,s=0..1,scaling=constrained,grid=[30,8]):

> a2:=rotate(a1,0,0,2*Pi/5):

> a3:=rotate(a1,0,0,4*Pi/5):

> a4:=rotate(a1,0,0,6*Pi/5):

> a5:=rotate(a1,0,0,8*Pi/5):

> a:=display(a1,a2,a3,a4,a5):b1:=reflect(a,[[0,0,0],[1,0,(sqrt(5)/2)+(1/2)],[1,1,(sqrt(5)/2)+(1/2)]]):

> b2:=rotate(b1,0,0,2*Pi/5):b3:=rotate(b1,0,0,4*Pi/5):b4:=rotate(b1,0,0,6*Pi/5):b5:=rotate(b1,0,0,8*Pi/5):

> c:=display(a,b1,b2,b3,b4,b5):cc:=reflect(c,[0,0,0]):

> p:=display(c,cc):

> p;

> vrml(p,"c:/Program Files/Maple 6/beauty/11-13.wrl",background_color=white);