Dodecagon Dissections

Author : Gavin Theobald

{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{9} Enneagon
{10} Decagon
{24} Icositetragon
{5/2} Pentagram
{6/2} Hexagram
{8/2} Octagram
{8/3} Octagram
{10/2} Decagram
{12/2} Dodecagram
{12/3} Dodecagram
{12/4} Dodecagram
{12/5}  Dodecagram
{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 6 10 6 11 10 1413 1211 1


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
12 9 9 12 14 1312 12  25 10

Triangle — Dodecagon (8 pieces)

Previously Ernest Irving Freese had discovered a different 8 piece solution.

This is a PP dissection.

There are many 8 piece solutions to this dissection, so it is disappointing that I have been unable to find anything better.

Square — Dodecagon (6 pieces)

Discovered by Harry Lindgren.

Pentagon — Dodecagon (10 pieces)

Hexagon — Dodecagon (6 pieces)

Discovered by Ernest Irving Freese.

This dissection and the following one use the method of completed tessellations. This dissects a hexagon with two small triangles to a dodecagon with the same two small triangles.

Hexagon — Dodecagon (6 pieces)

This 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.

Heptagon — Dodecagon (11 pieces)

Octagon — Dodecagon (10 pieces)

Enneagon — Dodecagon (14 pieces)

Enneagon — Dodecagon (13 pieces with 3 turned over)

Decagon — Dodecagon (12 pieces)

The two overlays show the strips before and after the modification of the decagon strip that saves a piece.

Decagon — Dodecagon (11 pieces with 2 turned over)

The two overlays show the strips before and after the modification of the decagon strip that saves a piece.

Dodecagon — Icositetragon {24} (25 pieces)

Dodecagon — Pentagram (12 pieces)

Dodecagon — Hexagram (9 pieces)

First discovered by Greg Frederickson.

Dodecagon — Octagram {8/2} (9 pieces)

Dodecagon — Octagram {8/3} (12 pieces)

Dodecagon — Decagram {10/2} (14 pieces)

Dodecagon — Dodecagram {12/2} (13 pieces)

Dodecagon — Dodecagram {12/2} (12 pieces with 1 turned over)

Dodecagon — Dodecagram {12/3} (12 pieces)

Dodecagon — Dodecagram {12/4} (25 pieces with 12 turned over)

Discovered by Greg Frederickson (2002).

Dodecagon — Dodecagram {12/5} (10 pieces)

Discovered by Greg Frederickson.

Dodecagon — Silver Rectangle (7 pieces)

Dodecagon — Golden Rectangle (7 pieces)

Discovered by Harry Lindgren.

Dodecagon — Domino (5 pieces)
Dodecagon — Optimised Rectangle (5 pieces)

Dodecagon — Greek Cross (6 pieces)

Discovered by Harry Lindgren.

Dodecagon — Latin Cross (7 pieces)

Discovered by Harry Lindgren (1951).