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--- problem:soccerballahedron [2013/08/14 13:01]
bmwoodruff
+++ problem:soccerballahedron [2013/08/14 13:50] (current)
bmwoodruff
@@ Line 1: / Line 1: @@
 ====== Soccerballahedron ======
 ==== Problem ====
-Construct the [[definition:Cayley graph]] of the group defined by the [[definition:group presentation]] $$\left< a,b\mid a^2=e, b^5=e, ababab=e\right>.$$
+Construct the [[definition:Cayley graph]] of the group defined by the [[definition:group presentation]] $$\left< a,b\mid a^2, b^5, ababab\right>.$$
+Can you think of a common object whose shape is similar to this graph?
 ----
@@ Line 7: / Line 8: @@
   * One option ends up with a soccerball.
   * This is a presentation for the [[definition:alternating group]] $A_5$.
+  * I decided to omit $=e$ from each relator.
 <sagecell>
 g = AlternatingGroup(5)
@@ Line 36: / Line 38: @@
   * [[http://www.lbl.gov/Science-Articles/Archive/MSD-C60-molecular-layer.html]]
-{{tag>problem ben}}
+{{tag>problem ben needsreview rben}}

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