I need embbeding K6 on orientable surface of genus 3 . but I was asked to do it with the next stipulation : 5 faces only and all the faces in the embedding will be pentagons . In my opinion the way to do it is to find planar representation to the orientable surface of genus 3 , and put k6 on him .. but I was tried many ways and could not find such embbeding .
just to be more clear about what I am talking about , I am attach sketch of k5 embbeding on torus (genus 1) , when in this time the requirement was to do it with 5 squares faces.
If you have any idea how to draw this embbeding I will be glad for some help
thank you !
Thanks