I think most of us were taught to lay our planes on their sides, as in the picture above, when placing them on the workbench. This is one of those myths that seem to be self-perpetuating. Set your planes sole down on your workbench. This will protect the sole of the plane and the iron from being inadvertently nicked by other metal tools that may be on the bench. If the sides of your bench plane get nicked it is not a problem, but nicks on the sole can leave plane tracks as can nicks on the iron.
It is not known where this myth began, but I wish it would go away.
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