Dodecagram Dissections

Author : Gavin Theobald

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{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{9} Enneagon
{10} Decagon
{12} Dodecagon
{5/2} Pentagram
{6/2} Hexagram
{8/2} Octagram
{8/3} Octagram
{10/2}  Decagram
{R√2} Silver Rectangle
{Rϕ} Golden Rectangle
{R2} Domino
{G} Greek Cross
{L} Latin Cross
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6 8 1211 8 11 12 14 12 1312


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 9 13 1413 17 1


Triangle — Dodecagram (6 pieces)

Discovered by Harry Lindgren (1964).


Square — Dodecagram (8 pieces)


Pentagon — Dodecagram (12 pieces)

Pentagon — Dodecagram (11 pieces with 3 turned over)

Compared to the other dodecagram dissections this one is particularly inefficient. This is due to the dimensions of the pentagon making it impractical to form a pentagon tessellation that can overlay a dodecagram tessellation.

By turning over pieces we can improve the dissection, but a entirely different technique is required if the dissection is to be improved further.


Hexagon — Dodecagram (8 pieces)

This is a modification of a dissection discovered by Greg Frederickson.


Heptagon — Dodecagram (11 pieces)


Octagon — Dodecagram (12 pieces)


Enneagon — Dodecagram (14 pieces)


Decagon — Dodecagram (12 pieces)


Dodecagon - Dodecagram Dodecagon - Dodecagram

Dodecagon — Dodecagram (13 pieces)

Dodecagon - Dodecagram Dodecagon - Dodecagram

Dodecagon — Dodecagram (12 pieces with 1 turned over)


Pentagram - Dodecagram Pentagram - Dodecagram

Pentagram — Dodecagram (14 pieces)


Hexagram — Dodecagram (9 pieces)

Discovered by Harry Lindgren (1964).


Octagram - Dodecagram Octagram - Dodecagram

Octagram {8/2} — Dodecagram (13 pieces)


Octagram {8/3} — Dodecagram (14 pieces)

Octagram {8/3} — Dodecagram (13 pieces with 1 turned over)


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


Silver Rectangle — Dodecagram (9 pieces)


Golden Rectangle — Dodecagram (9 pieces)


Domino — Dodecagram (9 pieces)


Greek Cross - Dodecagram Greek Cross - Dodecagram

Greek Cross — Dodecagram (10 pieces)


Latin Cross - Dodecagram Latin Cross - Dodecagram

Latin Cross — Dodecagram (11 pieces)

This dissection is a very, very tight fit!

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