Tetrahedralize Mesh

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Say I have a triangle mesh which forms the shell of an object which may not be convex. For every triangle, I have the vertices and a normal. I want to turn this mesh into a solid. I want to break up the geometry into a bunch of non-intersecting tetrahedra that fully fill the space. What algorithm could I use to do this?

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Look up "Tetrahedral mesh generation". There are many approaches, and many applications.