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.
Square - Pentagon (6 pieces)
This is not a very elegant solution because of the rather small piece, but it is another example of a TT22 dissection. There are a number of different six piece solutions possible and this raises the question of whether or not a five piece solution exists. There is a range of rectangle shapes that will dissect to a pentagon in just five pieces, but I think it unlikely that anyone will find a five piece solution for the square.
Pentagon - Hexagon (7 pieces)
Discovered by Harry Lindgren (1964).
Pentagon - Heptagon (9 pieces)
Pentagon - Octagon (9 pieces)
Pentagon - Octagon (8 pieces with 1 turned over)
Pentagon - Enneagon (10 pieces)
Pentagon - Decagon (9 pieces)
I nearly missed finding this dissection. The grey piece is no nearly cut into two, adding another two pieces to this dissection, that I did not think that it was possible. Fortunately I checked and hence obtained another record.
|
|
Pentagon - Hendecagon (12 pieces)
The overlay diagrams on the right show the basic dissection before I modify it to save some pieces.
Pentagon - Dodecagon (10 pieces)
There is room for improvement in this dissection. Is a 9 piece solution possible?
Pentagon - Pentagram (9 pieces)
Pentagon - Hexagram (8 pieces)
This is another example of a TT22 dissection.
Pentagon - Octagram (11 pieces)
Pentagon - Octagram (9 pieces)
The thin spike makes this a rather inelegant dissection, but I have not been able to find another 9 piece solution.
Pentagon - Dodecagram (12 pieces)
Compared to the other dodecagram dissections this one is particularly inefficient. This is due to the dimensions of the pentagon making it impractical to form a pentagon tessellation that can overlay a dodecagram tessellation.