2→3 and 3→2 Flips

A convex 5-vertex polyhedron has two valid tetrahedralizations. The first (Configuration 1) has two tetrahedra sharing a common face, and the second (Configuration 2) has three tetrahedra that all share a common edge.

Configuration 1 (2 tets)

Configuration 2 (3 tets)

Flipping Procedure

Every face-connected pair of elements is a candidate for a 2→3 flip, but the flip will only be valid of those two elements form a convex polyhedron. This can be checked by verifying that, for each of the 6 outer faces of the polyhedron, all the two non-face nodes lie on the same side of the face. Similarly, edges connected to three elements are candidates for a 3→2 flip if those three elements form a convex, 5-node polyhedron.