Sorry to disagree but my approach left you with your lines and a filled shape. The cusps are simply the lines (necessarily) folded back on themselves so it is arguable if the lines are not "preserved" as they do not form part of the changing of the shape body from this point.
As I can alter the line thickness and colour, I don't believe the lines are "absorbed" either.
I saw this to be the canonical form of what you needed.
@handrawn As you didn't include my approach to be a "grouped" one, is my shape one shape? I think it is.
Further, it is editable, though you have to manipulate the cusps separately.
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