Clebsch Graph
25 November, 2021
5-Colouring
55555
Loop Cycles
Gyre Multipliers
Growth
Single Tile Boundary Vertices
![55555-clebsch-graph_hyp.png](/static/6ea87fc013b857ae16e5b7baa3743d12/26378/55555_clebsch_graph_hyp_a6dd73d0b8.png)
Embedding
Notes
With an astonishing tile count of only 16 pentagonal tiles the Clebsch Graph manages to wind itself into a genus 5 surface with 960 orientation preserving automorphisms. Using the prototiles n-colouring, it is easy to identify the pentagonal prototile in the coloured euclidian embedding displayed above. Since all 16 5f prototiles share their edges, naturally every colour appears 8 times.
More information can be found at Wolfram Mathworld including an embedding matching the one above, albeit without colouring.