Enneagon Dissections

Author : Gavin Theobald

Triangle — Enneagon (8 pieces)

This dissection makes use of the TT2 method.

Previously Ernest Irving Freese found a 9 piece solution to this dissection. In Harry 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 am particularly pleased with it.

Square — Enneagon (9 pieces)

This was first dissected in 12 pieces by Ernest Irving Freese.

The first of these two dissections was my first solution of this dissection. It is a PP dissection. It suffers from having several short straight lines that do not show up clearly in diagrams of this size. Click on the diagrams to see an enlargement. The second solution is much more elegant. It is a TT2 dissection.

Pentagon — Enneagon (10 pieces)

This dissection uses the method of variable tessellation to give a very nice and very efficient dissection.

Hexagon — Enneagon (11 pieces)

Previously Harry Lindgren discovered a 14 piece solution. David Paterson found a 12 piece solution and Anton Hanegraaf found a different 11 piece solution.

This is a PP dissection.

Hexagon — Enneagon (10 pieces with 1 turned over)

This dissection uses the method of overlaid tessellations with the hexagon tessellation formed from a strip and with a variable enneagon tessellation. These methods combine to give a particularly efficient dissection.

Heptagon — Enneagon (13 pieces)

This dissection uses the method of variable tessellation.

Octagon — Enneagon (12 pieces)

This dissection overlays a variable enneagon strip over an octagon tessellation formed from strips.

Enneagon — Decagon (13 pieces)

This is a PP dissection.

Enneagon — Dodecagon (14 pieces)

This is a PP dissection.

Enneagon — Dodecagon (13 pieces with 3 turned over)

A piece is saved by combining dodecagon strips .

Enneagon — Octadecagon (19 pieces)

The basic method used by this dissection was discovered by Greg Frederickson but required turning over 9 pieces. I introduced the curved cuts to avoid this. The method works for all {n} to {2n} dissections.

Enneagon — Pentagram (14 pieces)

This is a PP dissection.

Enneagon — Hexagram (11 pieces)

This is a PP dissection.

Enneagon — Octagram {8/2} (15 pieces)

Enneagon — Octagram {8/3} (13 pieces)

This is a PP dissection.

Enneagon — Enneagram {9/2} (19 pieces)

The basic method used by this dissection was discovered by Greg Frederickson but required turning over 9 pieces. I introduced the curved cuts to avoid this. The method works for many {p} to {p/q} dissections.

Enneagon — Enneagram {9/3} (19 pieces with 9 turned over)

Discovered by Greg Frederickson. The method works for many {p} to {p/q} dissections but not for {9} to {9/4}.

Enneagon — Decagram {10/2} (17 pieces)

This is a PP dissection.

Enneagon — Dodecagram {12/2} (14 pieces)

See this page for an explanation of the method used.

Enneagon — Octadecagram {18/2} (17 pieces)

Enneagon — Silver Rectangle (9 pieces)

This is a TT2 dissection using a variable enneagon strip.

Enneagon — Golden Rectangle (9 pieces)

Previously Harry Lindgren discovered a 12 piece solution.

This is a PP dissection using a enneagon strip taken from a tessellation.

Enneagon — Domino (9 pieces)

This is a TT2 dissection using a variable enneagon strip.

Enneagon — Optimised Rectangle (7 pieces)

Enneagon — Greek Cross (11 pieces)

This is a TT2 dissection using a variable enneagon strip.

Enneagon — Latin Cross (10 pieces)

This is a TT2 dissection using a variable enneagon strip.