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Math Help - Cayley table

  1. #1
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    Cayley table

    Hi,

    i need help with drawing up a cayley table for an octagon.
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  2. #2
    MHF Contributor

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    I presume you mean the Cayley table for the group of symmetries for a regular octagon.

    First, how many elements are there in that group? There are the 8 rotations, of course, but then, since 8 is even, every line connecting two opposite vertices is a line of symmetry and every line bisecting a side is a line of symmetry. There are 4 pairs of opposite vertices and 4 pairs of parallel sides so there are a total of 8+ 4+ 4= 16 elements in this group and so [tex]16^2= 256 entries in the table.

    I recommend drawing a picture, carefully labeling each of the 16 symmetries and then working very carefully!
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