Pseudosphere
Sándor Kabai
Cylinders are used to build a solid pseudosphere.
Manipulate[Module[{},​​tract=ParametricPlot3D[{Sech[k],0,k-Tanh[k]},{k,-3.5,3.5},PlotStyle{Black}][[1]];​​tract1=Table[Rotate[tract,j2Pi/n,{0,0,1}],{j,n}];​​pseu=RevolutionPlot3D[{Sech[k],0,k-Tanh[k]},{k,-3.5,3.5},{v,0,-4.5},MeshNone][[1]];​​cones=​​Table[{Hue[0.8^10i],Cone[{​​{0,0,(ip-Tanh[ip])},​​{0,0,(ip-Tanh[ip])-((ip-Tanh[ip])-((i-1)p-Tanh[(i-1)p]))}​​},​​Sech[ip]]},{i,noc}];​​cyl=​​Table[{Cylinder[{​​{0,0,(ip-Tanh[ip])},​​{0,0,(ip-Tanh[ip])-((ip-Tanh[ip])-((i-1)p-Tanh[(i-1)p]))}​​},​​Sech[ip]]},{i,noc}];​​bottom=Rotate[{cones,cyl},Pi,{1,0,0}];​​​​Graphics3D[{If[spseu,pseu,{}],If[stract1,tract1,{}],Scale[cones,{1,1,0.999}],If[scyl,cyl,{}],If[sbottom,bottom,{}]},BoxedFalse,SphericalRegionTrue,ImageSize{300,400},ViewAngle0.1,ViewPoint{4,4,2},PlotRange{{-1,1},{-1,1},{-3,3}}]],​​{{p,0.25,"pitch"},0.1,0.3},​​{{noc,12,"frequency"},1,30,1},​​{{scyl,True,"cylinders"},{True,False},ControlPlacementLeft,ImageSizeTiny},​​{{stract1,True,"tractrix"},{True,False},ControlPlacementLeft,ImageSizeTiny},​​{{n,2,"No."},2,20,1,ControlPlacementLeft,ImageSizeTiny},​​{{sbottom,False,"bottom"},{True,False},ControlPlacementLeft,ImageSizeTiny},​​{{spseu,False,"pseuosphere"},{True,False},ControlPlacementLeft,ImageSizeTiny},​​TrackedSymbols->{p,noc,scyl,stract1,n,sbottom,spseu}]
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pitch
frequency
cylinders
tractrix
No.
bottom
pseuosphere
In[]:=
pseu=RevolutionPlot3D[{Sech[k],0,k-Tanh[k]},{k,-3.5,3.5},{v,0,Pi}][[1]];​​Graphics3D[pseu]
Out[]=