Thanks,
I don't know if this helps, S. McMillan wrote me the other day:
"Our Kohler Rialto (~12 yrs old K3402) started running about 2 years ago but could be stopped (until about 5 months ago) by tightening the top center screw of the ballcock to push down the plunger to stop the water flow. I saw online that Kohler no longer made the ballcock (refill valve) and I would have to buy a new toilet. A local plumbing supply house had them but they cost ~$98!!! Further online research has finally shown that this Kohler ballcock valve is Model 1B1-X made by Coast Foundries for Kohler. The top cap on ours says "Kohler Co. 1B1-X Sheath Ballcock". I found new 1B1-X ballcocks (~$24)and rebuild kits ($3.69) online at Ace hardware and DoItBest hardware stores. The new 1B1-X ballcocks don't have the lower flush float valve that feeds the rim flush so I purchased the rebuild kit at a local DoItBest hardware store (part number 450758 O/M 1-25) and repaired our old one in about 10 minutes. (Wouldn't it be nice if Kohler told us that a couple of years ago instead of telling us we needed to buy a new toilet)." S. McMillan
More information on the K-3402





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