Yes, ParametricRegion and ImplicitRegion can be an option. ParametricPlot3D function does not support thickness(range function).

Mathematica is plotting program, and now it support coming into 3D printing.

So I hope Mathematica support CAD like feature by mathematical function or intuitive editing.

Upper thickness 1mm and Lower base thickness 3mm(for example rr[x_] if x<0.5, 1<rr[x]<1.3 (3mm), if x>0.5 1<rr[x]<1.1 (1mm))Anyway thanks for intuitive opinion Hans Milton!

Thank you Hans Milton! Your reply was really helpful^^ I can now try 3D printing above stl file! Now I have one more question. Can I adjust the thickness of the 3D model by PlotTheme->"ThickSurface"? For example thinner like 1mm thickness or thicker just at the base part? (and thin middle and Cos[6t] part)

To get a solid STL model from a Mathematica surface plot you could try to use the option PlotTheme -> "ThickSurface" in the plot.

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Great Hans, you made a cycloid-zylo, using nested function definition!

Now I have exported the X-zylo and Cycloid zylo model into STL and tried to 3D Print it. However, no 3D program(Sketchup, Rhinocerus, Autodesk fusion 360, etc.) can recognize the mathematical plane into 3D printable object!

So this model need to have full thickness to be printed into real world^^ For example, the whole cylinder thickness 2 mm, and base thickness maybe 5mm with the height of 10mm(1/5 of whole height 50).

Please finally make a 3D full thickness X-zylo and cycloid-zylo model as well as STL if possible!

Your inspiration and mathematica spirit is really appreciated!

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Thank you for replies and great work for nice zylo design, Hans! Another triggering questions for some upgrade and real 3D Print!

First, How can I make thickness of the base zylo? Above Zylo has only plane, there is no thickness option in zylo and base or handle part of X-zylo.

Second question is a real tough one!! How can I make a cycloid on top of zylo instead of sine function in X-zylo? Because there is no known z-axis(height) explicit function of cycloid in terms of center axis, it's much triggering than X-zylo!! Is there any 3D-function to roll the following parametric pot into a cylinder?

ParametricPlot[{t - Sin[t], 1 - Cos[t]}, {t, 0, 10 Pi}]

This cycloid crown will be fantastic zylo if 3D-modeled by mathematica!!

Roll above on top of cylinder instead of ParametricPlot[{t, Sin[t]}, {t, 0, 10 Pi}]

Last remark concerning self-made zylos

xx[a_, h_] := {Cos[a], Sin[a], Min[h, 1 + Cos[5 a]/2]}
zz[a_, h_] := {Cos[a], Sin[a], Min[h, 1 + Cos[5 a]/2]}
pol[a_, h_, da_, dh_] := 
 Polygon[{xx[a, h], xx[a + da, h], zz[a + da, h + dh], zz[a, h + dh]}]

nda = 60; ndh = 20; ffh = .48;
da = 2 Pi/nda; dh = 2/ndh;
zylo = Table[{Hue[ffh n dh], 
    Table[pol[m da, n dh, da, dh], {m, 0, nda - 1}]}, {n, 0, ndh - 1}];
Graphics3D[zylo]

and

Animate[
 Graphics3D[Rotate[zylo, u, {0, 0, 1}]],
 {u, 0, 2 Pi}]

Poor man's solution (so it was done long long ago):

execute

Do[
Print[ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0, 1 + 1/2 Cos[5 t + u]}, PlotPoints -> 50, 
PlotRange -> All,  Mesh -> False, ColorFunction -> Function[{x, y, z}, Hue[.75 z]]]],
{u, 0, 2 Pi, .3}]

Double click on the second bracket from the right. All plots below the 1st one should vanish, and the bracket should be highlighted (in blue). Then press ctrl-shift -y

Try

ParametricPlot3D[{ Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0, 1 + 1/2 Cos[5 t]}, 
PlotPoints -> 50, PlotRange -> All, Mesh -> False]