Construct the Cayley graph of the group defined by the presentation $$\left< a,b\mid a^2, b^5, ababab\right>.$$

• One option ends up with a soccerball.
• This is a presentation for the alternating group $A_5$.

<sagecell> g = AlternatingGroup(5) d = g.cayley_graph(); d d.show(color_by_label=True, vertex_size=0.03, vertex_labels=False) show(g.semigroup_generators()) show(g.objgens()) #d.show3d(color_by_label=True, edge_size=0.01, edge_size2=0.02, vertex_size=0.03) #Uncomment the last line if you would like to allow java to draw the graph in 3D. # </sagecell>

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