Jason –
I had no great problem making the cavity in the slice like in your picture; maybe not in the most efficient way but it did work.
What I was unable to do, was stick the two slices together.
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Just looked, Dave –
Yes I see the sketch and model mirror types' difference.
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I think I see what you mean, Nick.
I'd envisaged that making the cavity on the complete block would have to done rather like sinking a blind screw-hole, from an outline circle on the face to be "drilled". I can do that as it is a nice simple cylinder, but this shape would not have worked like that. Or might but horrendously awkwardly.
I did not know you can Extrude Cut the middle of a solid. I had only known it as digging in from an external surface, like the drilled screw-hole.
Though also I don't know how to place an auxiliary plane within a figure, then using it. I tried that first step, experimenting with an existing model, but without success.
"dodgy thinking" ? Aye, it's called ignorance, inexperience and confusion. Plus being very slow to learn anything (that's always been so).