In the attached scene file you'll see 3 branches doing the same, centroid tripling: - Half-edges VEX solution, by Jake Rice. - Inset, Primitive Scale to 0, Fuse. - Inset and Edge Collapse.
If someone wants to help, let me know if the third branch locks Houdini for you as it does for me. If not try 200x200 sphere. It's a shame because it's the most straight forward one.