Problem: How countless lines the symmetry walk a consistent octagon have?
I"d say over there is 8 .Drawing one octagon is ideal but if you desire to do without it , imagine illustration symmetric present inbetween the lines of the Octagon or you have the right to imagine illustration lines in ~ the suggest where that the 2 currently meet.
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Lines attracted inbetween present = 4Lines attracted where 2 points meet = 4Total = 8
For n-gons over there are constantly $2n$ symmetries in total; $n$ reflections and also $n$ rotations. For this reason in this case there are 16 symmetries in total, 8 reflections and also 8 rotations.
A nice method to think about this is to take into consideration where you have the right to put each vertex. A the opposite is any kind of permutation the preserves adjacency the vertices. Label the vertices 1 with to 8, climate you have actually 8 choices for whereby to placed the an initial vertex, 2 for the next and also only 1 ~ that. Hence we have 16 symmetries.
If girlfriend want an ext information ~ above this look increase Dihedral groups.
My prize I obtained was 10 because if you draw lines threw the octagon due to the fact that it will explain an ext to you. - soon grader advice
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