10 Construct six spheres of the same size each touching four others.

> restart:

> with(plottools):

> a1:=sphere([1,1,0],1,grid=[35,35],color=yellow):

> a5:=sphere([-1,1,0],1,grid=[35,35],color=green):

> a6:=sphere([-1,-1,0],1,grid=[35,35],color=brown):

> a2:=sphere([1,-1,0],1,grid=[35,35],color=pink):

> a3:=sphere([0,0,2^(1/2)],1,grid=[35,35],color=blue):

> a4:=sphere([0,0,-2^(1/2)],1,grid=[35,35],color=red):

> with(plots):

Warning, the name changecoords has been redefined

11 Construct twelve spheres of the same size each touching five others.

> restart:

> with(plottools):

> r:=sqrt(5)/2-1/2:

> x:=r:y:=1:

> a1:=sphere([0,x,y],r,grid=[35,35],color=yellow):

> a2:=sphere([0,x,-y],r,grid=[35,35],color=green):

> a3:=sphere([0,-x,y],r,grid=[35,35],color=brown):

> a4:=sphere([0,-x,-y],r,grid=[35,35],color=pink):

> a5:=sphere([y,0,x],r,grid=[35,35],color=blue):

> a6:=sphere([y,0,-x],r,grid=[35,35],color=red):

> a7:=sphere([-y,0,x],r,grid=[35,35],color=gold):

> a8:=sphere([-y,0,-x],r,grid=[35,35],color=cyan):

> a9:=sphere([x,y,0],r,grid=[35,35],color=orange):

> a10:=sphere([x,-y,0],r,grid=[35,35],color=grey):

> a11:=sphere([-x,y,0],r,grid=[35,35],color=coral):

> a12:=sphere([-x,-y,0],r,grid=[35,35],color=magenta):

> with(plots):

Warning, the name changecoords has been redefined

12 Construct twenty spheres of the same size each touching three others.

> restart:

> with(plottools):

> q:=sqrt(5)/2+1/2:p:=2*Pi/5:r:=2*sin(p/2):

> a1:=sphere([2*cos(p),2*sin(p),q+1],r,grid=[35,35],color=yellow):

> a2:=sphere([2*cos(2*p),2*sin(2*p),q+1],r,grid=[35,35],color=green):

> a3:=sphere([2*cos(3*p),2*sin(3*p),q+1],r,grid=[35,35],color=brown):

> a4:=sphere([2*cos(4*p),2*sin(4*p),q+1],r,grid=[35,35],color=pink):

> a5:=sphere([2*cos(5*p),2*sin(5*p),q+1],r,grid=[35,35],color=blue):

> a6:=sphere([2*q*cos(p),2*q*sin(p),q-1],r,grid=[35,35],color=red):

> a7:=sphere([2*q*cos(2*p),2*q*sin(2*p),q-1],r,grid=[35,35],color=gold):

> a8:=sphere([2*q*cos(3*p),2*q*sin(3*p),q-1],r,grid=[35,35],color=cyan):

> a9:=sphere([2*q*cos(4*p),2*q*sin(4*p),q-1],r,grid=[35,35],color=orange):

> a10:=sphere([2*q*cos(5*p),2*q*sin(5*p),q-1],r,grid=[35,35],color=grey):

> a11:=sphere(-[2*cos(p),2*sin(p),q+1],r,grid=[35,35],color=yellow):

> a12:=sphere(-[2*cos(2*p),2*sin(2*p),q+1],r,grid=[35,35],color=green):

> a13:=sphere(-[2*cos(3*p),2*sin(3*p),q+1],r,grid=[35,35],color=brown):

> a14:=sphere(-[2*cos(4*p),2*sin(4*p),q+1],r,grid=[35,35],color=pink):

> a15:=sphere(-[2*cos(5*p),2*sin(5*p),q+1],r,grid=[35,35],color=blue):

> a16:=sphere(-[2*q*cos(p),2*q*sin(p),q-1],r,grid=[35,35],color=red):

> a17:=sphere(-[2*q*cos(2*p),2*q*sin(2*p),q-1],r,grid=[35,35],color=gold):

> a18:=sphere(-[2*q*cos(3*p),2*q*sin(3*p),q-1],r,grid=[35,35],color=cyan):

> a19:=sphere(-[2*q*cos(4*p),2*q*sin(4*p),q-1],r,grid=[35,35],color=orange):

> a20:=sphere(-[2*q*cos(5*p),2*q*sin(5*p),q-1],r,grid=[35,35],color=grey):

> with(plots):

Warning, the name changecoords has been redefined

13 Construct twelve spheres of the same size each touching four others.

>

> restart:

> with(plots):with(plottools):

Warning, the name changecoords has been redefined

> a1:=sphere([1,0,1],p,color=yellow):

> a2:=sphere([0,1,1],p,color=red):

> a3:=sphere([-1,0,1],p,color=green):

> a4:=sphere([0,-1,1],p,color=coral):

> a5:=sphere([1,0,-1],p,color=grey):

> a6:=sphere([0,1,-1],p,color=magenta):

> a7:=sphere([-1,0,-1],p,color=orange):

> a8:=sphere([0,-1,-1],p,color=blue):

> a9:=sphere([1,1,0],p,color=pink):

> a10:=sphere([1,-1,0],p,color=cyan):

> a11:=sphere([-1,-1,0],p,color=gold):

> a12:=sphere([-1,1,0],p,color=brown):

> display(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,scaling=constrained);

>