I can do this trouble by illustration a picture and present of symmetry. Mine question about this trouble is what if that is not an octagon, but any regular polygon. What is a simple way to settle the problem?

Problem: How countless lines of symmetry walk a constant octagon have?


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I"d say over there is 8 .Drawing an octagon is finest but if you want to do without that , imagine drawing symmetric lines inbetween the currently of the Octagon or you can imagine drawing lines at the suggest where of the 2 currently meet.

You are watching: How many lines of symmetry does a regular octagon have

Lines drawn inbetween currently = 4Lines drawn where 2 points accomplish = 4Total = 8


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For n-gons over there are constantly $2n$ symmetries in total; $n$ reflections and also $n$ rotations. For this reason in this case there room 16 symmetries in total, 8 reflections and also 8 rotations.

A nice means to think around this is to take into consideration where you can put each vertex. A symmetry is any kind of permutation that preserves adjacency that vertices. Label the vertices 1 through to 8, climate you have actually 8 options for wherein to put the an initial vertex, 2 for the next and also only 1 after that. For this reason we have actually 16 symmetries.

If friend want an ext information on this look up Dihedral groups.


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My price I got was 10 since if you attract lines threw the octagon due to the fact that it will explain much more to you. - soon grader advice


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