Cayley diagrams of groups of genus 0
On bounded pieces of plane

C1



C2


These would fit better on a cylinder
Those shown here are all based on 7. Similar diagrams exist
for any other integer.

C7



C7×C2



D14



D14



D14


These would fit better on a sphere

C2×C2



C2×C2



C2×C2×C2



D8



D8



A4



A4



A4



S4



S4



S4



S4



S4



S4×C2



A5



A5



A5



A5



A5×C2


Covering the whole plane
I do not know what groups these portray.
Click on any of these to see a larger region of the infinite plane.
On a bounded infinite strip of the plane
The groups portrayed are specified to the left.
ℤ  
ℤ  
ℤ  
ℤ×C2  
ℤ×C2  
Dℤ  
Dℤ  
Dℤ  
Qℤ  
Qℤ  
Qℤ  
Some more Cayley diagrams drawn on surfaces appropriate to their genus.
Some more Cayley diagrams
and other pages on groups
Copyright N.S.Wedd 2009