I deserve to do this trouble by illustration a photo and present of symmetry. My question about this trouble is what if the is not an octagon, but any regular polygon. What is a simple means to solve the problem?

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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