Before revision:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending  G on the way  , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
After revision:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending G on the way (exploiting its mild flexibility) , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.