Appearance as a symbol of class makes such a regime quite easy to dismantle.
What An Buchen did was simple: just exterminate these polygons with numerous sides. By dealing with these, and without anyone to lead the remaining polygons, they could hardly amount to anything significant—thus they'd no longer pose any threat to the unification of the Flat Kingdom.
When it came to taking resolute, sweeping actions, Li Geng was far from An Buchen's equal. While he still hesitated, An Buchen had already raised the butcher's knife.
Kill, kill, kill, all the way across the board, she didn't bother to distinguish between good and evil polygons, merely decreeing the same end for all of them.
On one hand, she didn't have the time to concern herself with whether these polygons were good or bad, and on the other hand, she had always adhered to one concept:
The meat-eaters are despised.
It had been so from birth, irrespective of one's personal notions of good and evil.