Can we spherify a cluster of vertices?

[toontje]

Yep, select those vertices. Snap cursor to vertices. The cursor should be in the center of the vertex cluster. Go to a side view to place the cursor a little outside the selection. Hit " to sphere" then 100% to spherize your selection.

Or

you can add a UV sphere object and then you should use the shrinkwrap modifier which is fairly self explanatory.

[fktt]

select the vertices, make sure the 3D cursor is snapped to the selections center
(eg. lets say your selection is a subdivided cube),
and hit ctrl+shift+S in 2.49 or alt+shift+S in 2.5,
and move your mouse cursor accordingly.

[javierdl]

Thanks a bunch to both, guys! :)
"To Sphere" did the job.
I should tinker around with the Shrinkwrap mod eventually. It does look very good for many purposes.

Happy new year!

JDL

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