Glad to help!

For export try:

s3D = ContourPlot3D[
  clebsch[x, y, z] == 0, {x, y, z} \[Element] Ball[{0, 0, 0}, 1], 
  PlotTheme -> "ThickSurface", Axes -> False, Boxed -> False, 
  PlotPoints -> 50, RegionBoundaryStyle -> None]

Printout3D[Graphics3D[s3D[[1, 1]]], RegionSize -> Quantity[10, "Centimeters"]]

This will throw some error messages, but it seems to work, though! I have no idea on how to adjust the wall thickness.

Using s3D[[1, 1]] instead of simply s3D (i.e. extracting GraphicsComplex) was the only workaround I could find to make it work on MMA V12.1 - the new introduced RegionBoundaryStyle seems to be the problem (at least for me ("12.1.0 for Linux x86 (64-bit) (March 14, 2020)")).

Addendum: Case reported [CASE:4546899]

On the mentioned website they are using a different formula! And to get the same shape you can do:

clebsch[x_, y_, z_] := 81 (x^3 + y^3 + z^3) - 
  189 (x^2*y + x^2 z + y^2 x + y^2 z + z^2 x + z^2 y) + 54 (x y z) + 
  126 (x y + x z + y z) - 9 (x^2 + y^2 + z^2) - 9 (x + y + z) + 1
ContourPlot3D[clebsch[x, y, z] == 0, {x, y, z} \[Element] Ball[{0, 0, 0}, 1]]

Thank You so much Henrik!

So weird that I didn't see that. The other mistake I made: I wasn't on Alpha-Mode Notebook, but a regular one. I would like to increase the range for plotting, so I tried to enter this formula, but it can't understand what I am saying

plot3D 81 (x^3 + y^3 + z^3) - 9 (x^2 + y^2 + z^2) - 189 (x^2 y + x^2 \ z + x y^2 + x z^2 + y^2 z + y z^2) + 54 x y z - 9 (x + y + z) + 126 \ (x y + x z + y z) - 1 = 0, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}]

Then I tried to increase the limits in the formula You gave, but still there is some error.

EDIT: I got the limits fixed. Thnk You!

Though I was hoping it would look something like this: