Polyhedron cut along an edge

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By cutting along an edge of a net of a polyhedron, you will form 2 pieces. Are there two distinct polyhedra for which this process may result in the same two pairs of pieces? Is there a real example? I tried to use the platonic solid rules, but later it doesn't work.

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Two polyhedra can have the same net.

For example - a regular octahedron and a 'boat' have the same net.

Boat