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 Isosceles from Regular (Posted on 2012-01-20)
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: Equilateral triangle are certainly isosceles. | Comment 11 of 13 |
(In reply to Equilateral triangle are certainly isosceles. by Jer)

In that case, I will postulate that any regular n-gon where n can be expressed as 2^k+2^p (where k and p are integers >=0, but not both 0) can be dissected as required in the problem.

Here's a short list up to 100:

`n  k  p3  1  0 (assuming a regular triangle is okay with 0 "dissections")4  1  15  2  06  2  18  2  29  3  010 3  112 3  216 3  317 4  018 4  120 4  224 4  332 4  433 5  034 5  136 5  240 5  348 5  464 5  565 6  066 6  168 6  272 6  380 6  496 6  5`

In other words, it looks like A173786

Still don't know if this would be the complete list, or if it misses some ns.

Edited on January 21, 2012, 5:02 pm

Edited on January 21, 2012, 5:02 pm
 Posted by Dustin on 2012-01-21 16:55:03

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