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This may surprise you but the above-mentioned DMT8C (325 grit) or the Atoma 400 both are just fine (pun intended) for lapping a 12k synthetic hone.

I tried to go that route years ago and found that the tile was far from flat so check it with a straight edge (you should be able to find one since you're in a home improvement store) before...

W/D sandpaper or loose silicon carbide on a flat surface--ideally in a container. Whether you need to do it before first use will depend on whether or not yours comes flat. You can check this with...

They work. They're not the best but they do work. You do have to make sure that they are flat and they have a tendency to leave deeper scratches than a diamond plate. Also, with use, you need to...