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This work demonstrates some novel procedures for joining multiple solutions of the Einstein field equation in a way which creates a new analytical tool for studying them. Joining known solutions along shells ensures that we have solutions off the boundary. In 1985 Dray and 't Hooft showed how to use use spherically symmetric shells of massless matter to join spacetime regions with Schwarzschild geometry. We demonstrate here how to use these solutions to draw information-rich Penrose diagrams usable for investigating the characteristics of the solutions.