Step 4 of 6: Stop at the last triangle
In plain words
A shrinking process that always removes at least one piece cannot run forever on a finite pile; it must stop, and the only shape small enough to stop at is the humble single triangle sitting inside its own outer region.
Detailed analysis
Because every removal strictly shrinks the graph, the stripping process must eventually terminate, and it can only terminate when a single triangle is left: three vertices, three edges, and two faces — the triangle itself and the surrounding outer region. For this smallest possible graph, .