Octagonal 1024-fold Symmetry Expansion

With only 36 octagonal tiles this tilegraph wraps around a skeleton of interconnected hexagons to end up forming a surface of genus 19. The obvious size of the group of the dual graph of 36 expands 1'024-fold in the actual vertex group of the tilegraph that ends up at 36864 automorphisms. The petrie polygons all have a length of 24 edges. The n-coloring of the tile is one of 4 octagonal n-colorings that allow for constructing tilegraphs where the tiles and petrie polygons have the same size (8) and same coloring. Even though this is not the case for the tilegraph at hand, tilegraphs grown using these n-colorings tend to show very high symmetry.