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Isosceles from Regular (Posted on 2012-01-20) Difficulty: 3 of 5
Which regular polygons can be dissected into isosceles triangles by non-intersecting diagonals?

See The Solution Submitted by Jer    
Rating: 5.0000 (1 votes)

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re: Not sure if this is what you want - A rewrite. | Comment 2 of 13 |
(In reply to Not sure if this is what you want by Larry)

You know, I wish someone had caught this in the queue.  I really like how concise the original is but you pointed out a big flaw.    The problem is the term non-intersecting.  Intersections at the vertices of the polygon I meant to allow.  So your hexagon example is fine.  Actually I think your square example is the only case where the diagonals don't share any endpoints.

As for the term dissected, the term generally means completely split up.  Otherwise any n-gon can be split into an isosceles triangle and an (n-1)-gon.

So here's the (hopefully better) version:

Which regular polygons can be dissected into isosceles triangles by diagonals that may only intersect at their endpoints?



  Posted by Jer on 2012-01-21 00:05:43

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