The honing tool (50) has a hub section for connection to a drive part and peripherally uniformly distributed teeth (52), and the planing tool (56) has a hub section for connection to a bearer spindle and peripheral uniformly distributed teeth (58) with grinding particles, esp. diamond particles. The axial pitch and width of the teeth (58,52) of the planing tool and honing tool are matched so that there are always more than one point of engagement between the tools. Independent claims are also included for a honing tool and a sharpening machine.
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