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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: 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  p
3  1  0 (assuming a regular triangle is okay with 0 "dissections")
4  1  1
5  2  0
6  2  1
8  2  2
9  3  0
10 3  1
12 3  2
16 3  3
17 4  0
18 4  1
20 4  2
24 4  3
32 4  4
33 5  0
34 5  1
36 5  2
40 5  3
48 5  4
64 5  5
65 6  0
66 6  1
68 6  2
72 6  3
80 6  4
96 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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