Hexagon Dissections

Triangle — Hexagon (5 pieces)

This uses the TT2 method. I know of no other 5 piece solution to this dissection.

Discovered by Harry Lindgren (1961).

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)

This is a PP dissection.

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)

This dissection uses the method of completed tessellations. This dissects a hexagon with two small triangles to a dodecagon with the same two small triangles.

The first solution is nicely symmetric, but the second is different to other published solutions in the use of curved pieces. Without the curved pieces it would be necessary to turn over two of the pieces.

Hexagon — Tetradecagon (11 pieces)
Hexagon — Tetradecagon (10 pieces with 1 turned over)

Hexagon — Hexadecagon (12 pieces)

Hexagon — Octadecagon (12 pieces)

This dissection uses the method of completed tessellations. This dissects a hexagon with two small triangles to a dissected octadecagon with the same two small triangles.

Hexagon — Icosagon (13 pieces)

Hexagon — Pentagram (9 pieces)

Hexagon — Hexagram (6 pieces)

This dissection uses the method of completed tessellations. This dissects a hexagon with two small triangles to a hexagram with the same two small triangles.

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} (9 pieces)

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} (10 pieces)

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).