Hexagon Dissections

Author : Gavin Theobald

{3}	Triangle
{4}	Square
{5}	Pentagon
{7}	Heptagon
{8}	Octagon
{9}	Enneagon
{10}	Decagon
{11}	Hendecagon
{12}	Dodecagon
{18}	Octadecagon
{5/2}	Pentagram
{6/2}	Hexagram
{8/2}	Octagram
{8/3}	Octagram
{12/2}	Dodecagram
{R}	Golden Rectangle
{G}	Greek Cross
{L}	Latin Cross

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 following more complex dissection for the 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.

Pentagon - Hexagon (7 pieces)

Discovered by Harry Lindgren (1964).

Hexagon - Heptagon (8 pieces)

Hexagon - Octagon (8 pieces)

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 2 turned over)

Hexagon - Dodecagon (6 pieces)

There are other solutions to this dissection in 6 pieces obtainable from the tessellations on the right, but this one is different to other published solutions in the use of curved pieces.

Hexagon - Octadecagon (12 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.