Triangle — Hexagon (5 pieces)
Discovered by Harry Lindgren (1961).
I know of no other 5 piece solution to this dissection.
Square — Hexagon (5 pieces)
This new dissection is unusual in that there are aligned edges of the square
and the hexagon. I found this dissection after finding the more complex dissection
of the square and heptagon. The hexagon strip can be formed in a
variety of ways. The trick is to form it the correct way so that when the
two strips are overlaid, a hexagon edge coincides with a square edge, hence
saving a piece.
The dissection is translational.
Pentagon — Hexagon (7 pieces)
Discovered by Harry Lindgren (1964).
Hexagon — Heptagon (8 pieces)
Hexagon — Octagon (8 pieces)
Hexagon — Octagon (7 pieces with 2 turned over)
Hexagon — Enneagon (11 pieces)
Hexagon — Enneagon (10 pieces with 1 turned over)
Hexagon — Decagon (9 pieces)
Hexagon — Decagon (8 pieces with 3 turned over)
Hexagon — Hendecagon (12 pieces)
Hexagon — Hendecagon (11 pieces with 1 turned over)
Hexagon — Dodecagon (6 pieces)
The first solution is nicely symmetric, but the second is different to
other published solutions in the use of curved pieces.
Hexagon — Tetradecagon (11 pieces)
Hexagon — Tetradecagon (10 pieces with 1 turned over)
Hexagon — Hexadecagon (12 pieces)
Hexagon — Octadecagon (12 pieces)
Hexagon — Icosagon (13 pieces)
Hexagon — Pentagram (9 pieces)
Hexagon — Hexagram (6 pieces)
This is my favourite dissection! Greg Frederickson found a similar dissection, but his
requires two pieces to be turned over. His solution is given by the overlay on the right.
But by extending the two pieces that are turned over using arcs creates two symmetric pieces
that no longer need turning over. The same trick can be used for other dissections, but this
is the only straight sided dissection known for which curved pieces are essential for an
optimum solution.
Hexagon — Heptagram {7/2} (11 pieces)
Hexagon — Heptagram {7/2} (11 pieces with 2 turned over)
Hexagon — Octagram {8/2} (10 pieces)
Hexagon — Octagram {8/2} (9 pieces with 1 turned over)
Hexagon — Octagram {8/3} (9 pieces)
Hexagon — Octagram {8/3} (8 pieces with 1 turned over)
The second of these two dissections is a very tight fit! Solving this in just
eight pieces was a surprise.
Hexagon — Enneagram {9/2} (13 pieces)
Hexagon — Enneagram {9/3} (9 pieces)
Hexagon — Enneagram {9/3} (8 pieces with 2 turned over)
Hexagon — Decagram {10/2} (11 pieces)
Hexagon — Decagram {10/2} (10 pieces with 2 turned over)
Hexagon — Dodecagram {12/2} (8 pieces)
This is a modification of a dissection discovered by Greg Frederickson.
Hexagon — Dodecagram {12/3} (13 pieces)
Hexagon — Dodecagram {12/3} (12 pieces with 3 turned over)
Hexagon — Silver Rectangle (5 pieces)
The dissection is translational.
Hexagon — Golden Rectangle (5 pieces)
The dissection is translational.
Hexagon — Domino (5 pieces)
The dissection is translational.
Hexagon — Optimised Rectangle (3 pieces)
The dissection is translational. Each piece has the same area.
Hexagon — Greek Cross (7 pieces)
Hexagon — Latin Cross (6 pieces)
Discovered by Harry Lindgren (1961).