Triangle - Square (4 pieces)
The discovery of this dissection is normally attributed to Herny Ernest Dudeney (1902) but may have been first discovered by C. W. McElroy (1902).
Triangle - Pentagon (6 pieces)
This is perhaps not the best example of a dissection of triangle and pentagon, but it is new and it does demonstrate the TT22 technique.
Triangle - Hexagon (5 pieces)
Discovered by Harry Lindgren (1961).
I know of no other 5 piece solution to this dissection.
Triangle - Heptagon (8 pieces)
Triangle - Octagon (7 pieces)
Triangle - Enneagon (8 pieces)
Previously Freese found a 9 piece solution to this dissection. In Lindgren's book he states "The conclusion is that if you can beat Freese, you will have found a needle in a haystack". I found the needle! This was one of the first dissection improvements that I found, and I was particularly pleased with it.
Triangle - Decagon (7 pieces)
I'm very pleased with this dissection. It's the only dissection in which I use this particular decagon strip.
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Triangle - Hendecagon (11 pieces)
Reducing this dissection to 11 pieces was not easy. In the wider hendecagon strip the two large pieces can be varied in size. I vary the size to ensure that a hendecagon edge passes exactly through the intersection of triangle edges at the edge of the triangle strip. This saves a piece. The second overlay diagram shows the initial stage of overlaying the second two strips. I modify the shape of the trapezium of the thinner triangle strip to save a further two pieces.
Triangle - Dodecagon (8 pieces)
It is disappointing that this dissection requires as many as 8 pieces, but I've been unable to find anything better.
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Triangle - Tridecagon (12 pieces)
Triangle - Tetradecagon (12 pieces)
Triangle - Pentagram (7 pieces)
Triangle - Hexagram (5 pieces)
Triangle - Heptagram {7/3} (12 pieces)
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Triangle - Octagram (9 pieces)
This was another dissection that was particularly hard to find. A ten piece dissection was fairly straightforward, but every trick I tried to use to improve the dissection further failed. Finally I found the above dissection. The overlaying of strips shown is not sufficient on its own. A further trick is required to save the last piece.
Triangle - Octagram (8 pieces)
Triangle - Decagram {10/2} (11 pieces)
There may well be a 10 piece solution to this dissection.
Triangle - Decagram {10/4} (10 pieces)
Triangle - Dodecagram {12/2} (6 pieces)
Discovered by Harry Lindgren (1964).