Clebsch Graph

Clebsch Graph

25 November, 2021

5-Colouring

55555

n-colouring 55555

Loop Cycles

\((f_1,f_4,f_5,f_3)\;\)\(2\mathord*(f_2,f_4)\;\)\(2\mathord*(f_1,f_5)\;\)

Gyre Multipliers

\(-\)

Growth

Single Tile Boundary Vertices

Topology Type

Toroidal

Skeleton Type

Unknown

Files

graphML Download

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.