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I have failed for the last two hours in making a disk with perfect semicircular edges like this image

https://www.pinterest.de/pin/155303887140848301/

I was trying to make a very short cylinder and then Bevel upper and lower faces, but that produces an edge with a different curvature than a semicircular edge.

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    $\begingroup$ You probably didn't apply the scale to that cylinder, that's why the bevel didn't produce the expected result. $\endgroup$ – metaphor_set May 29 at 0:24
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You could think of the discs as a doughnuts with their tops and bottoms filled in..

enter image description here

  • Alt - select the midway loops of a torus, created by with the appropriate major and minor radii
  • V - drag rip the edges and hover-L select the inner faces
  • X delete them, Reselect the boundary loops
  • F fill the top and bottom
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I added a cylinder with Depth of 0.1m

Cylinder

Tn edit mode tab I selected top and bottom faces.

Faces

I used bevel tool Ctrl+B to bevel (with 16 segments) for 0.05m. In the bottom left of the viewport there is a window that allows you to type values by keyboard. If you left click anywhere after beveling it will disappear!

Beveled

This shows curvature of this disk compared to 64 segment circle with radius of 0.05m.

Circle

Thanks to @Jachym Michal for this tip. We accidentally created some duplicated vertices and edges in the very middle. They might cause problems with rendering. It's very easy to remove them. When we are in edit mode we select everything with A and then press Alt+M and chose By Distance from merge menu. You should not see any change, but duplicated vertices are gone!

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