Octagonal 18432-fold Symmetry Expansion

It's embedding does not reflect the incredible number of symmetries of this tilegraph. 16 octagonal tiles form a surface of genus 9. The tilegraph has 294'912 automorphisms. This enormous difference in symmetry between dual and vertexgraph is suspected to stem from the fact that the petrie polygons also are pf length 8 and are colored exactly the same as the regular tiles. Mainly, a feature of the underlying n-coloring and to a certain degree the right choice of glueing rules, which decides the size of the petrie polygons.

Interestingly the dualgraph can be read as a rhombic dodecahedron with two "inner" vertices or 6 interconnected cubes.

The skeleton graph (shown "black" above) underlines the relationship with the tilegraph Octagonal 1024-fold Symmetry Expansion which only differs by one glueing rule creating its hexagonal structure as opposed to the quadratic structure this tilegraph.