Here are the three equations that (parametrically) generate the umbilic torus that appears on the cover of our Cal I text book:

> z := sin(u)*((7.+cos(u/3-2*v)+2*cos(u/3+v)));

> y := cos(u)*((7.+cos(u/3-2*v)+2*cos(u/3+v)));

> x := sin(u/3-2*v) + 2.*sin(u/3+v);

> for i to 12 do p.i:=plot3d([x,y,z],u=-Pi..Pi,v=-Pi..Pi,orientation=[30*i,90]) od:

> plots[display]([seq(p.i,i=1..12)],insequence=true);

>

You could do it this way: multiply your parametric expressions by the 3x3 rotation matrix .

> plots[animate3d]([cos(k)*x+sin(k)*y,-sin(k)*x+cos(k)*y,z],u=-Pi..Pi,v=-Pi..Pi,k=-Pi..Pi);

>