Cayley diagrams of groups of genus 0
On bounded pieces of plane
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C1
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C2
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These would fit better on a cylinder
Those shown here are all based on 7. Similar diagrams exist
for any other integer.
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C7
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C7×C2
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D14
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D14
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D14
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These would fit better on a sphere
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C2×C2
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C2×C2
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C2×C2×C2
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D8
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D8
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A4
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A4
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A4
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S4
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S4
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S4
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S4
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S4
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S4×C2
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A5
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A5
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A5
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A5
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A5×C2
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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 | |
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| ℤ | |
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| ℤ | |
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| ℤ×C2 | |
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| ℤ×C2 | |
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| Dℤ | |
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| Dℤ | |
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| Dℤ | |
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| Qℤ | |
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| Qℤ | |
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| Qℤ | |
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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
