Enneagon Dissections

Author : Gavin Theobald

{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{10} Decagon
{12} Dodecagon
{18} Octadecagon
{5/2} Pentagram
{6/2} Hexagram
{8/2} Octagram
{8/3} Octagram
{9/2} Enneagram
{9/3} Enneagram
{10/2} Decagram
{12/2} Dodecagram
{18/2}  Octadecagram
{R√2} Silver Rectangle
{Rϕ} Golden Rectangle
{R2} Domino
{R×} Optimised Rectangle
{G} Greek Cross
{L} Latin Cross
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
8 9 10 1110 13 12 1 13 1413 19


5/2 6/2 7/2 7/3 8/2 8/3 9/2 9/3 9/4 10/2 10/3 10/4 12/2 12/3 12/4 12/5
14 11 15 13 19  19 17 14


Triangle — Enneagon (8 pieces)

This dissection makes use of the TT2 technique.

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)


Hexagon — Enneagon (11 pieces)

Hexagon — Enneagon (10 pieces with 1 turned over)


Heptagon — Enneagon (13 pieces)


Octagon — Enneagon (12 pieces)


Enneagon — Decagon (13 pieces)


Enneagon — Dodecagon (14 pieces)

Enneagon — Dodecagon (13 pieces with 3 turned over)


Enneagon — Octadecagon (19 pieces)


Enneagon — Pentagram (14 pieces)


Enneagon — Hexagram (11 pieces)


Enneagon — Octagram {8/2} (15 pieces)


Enneagon — Octagram {8/3} (13 pieces)


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


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

Discovered by Greg Frederickson (2002).


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


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


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


Enneagon — Silver Rectangle (9 pieces)


Enneagon — Golden Rectangle (9 pieces)


Enneagon — Domino (9 pieces)


Enneagon — Optimised Rectangle (7 pieces)


Enneagon — Greek Cross (11 pieces)


Enneagon — Latin Cross (10 pieces)