Step 5 of 6: Conclude that V − E + F = 2 for the original polyhedron
In plain words
Think of as a chip on a gaming table that nobody is allowed to touch: every move in the game (flattening, cutting a diagonal, peeling a triangle) leaves the chip exactly where it was. Once the game ends with a single triangle and a visible chip value of , that must have been its value from the very first move.
Detailed analysis
Every operation used along the way — flattening, triangulating, and removing triangles — left unchanged, and the final graph gives . Since the quantity never changed during the reduction, it must already have equalled for the flattened graph, and hence for the original convex polyhedron.
- Invariant
- A quantity that stays exactly the same throughout a sequence of operations, even though the object it is computed from keeps changing.