Describe how 12 identical pipes are joined together symmetrically.

> restart;

> tau:=(sqrt(5)+1)/2:

> with(plots):with(plottools):

Warning, the name changecoords has been redefined

> x:=cos(t):

> y:=sin(t):

> u:=x*tau:

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

> a1:=plot3d([x,y,z],t=-Pi/5..Pi/5,s=0..1,scaling=constrained,grid=[20,8]):

> 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,tau],[1,1,tau]]):

> 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]):

> display(c,cc);

>