Decagon Dissections

Author : Gavin Theobald

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{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{9} Enneagon
{12} Dodecagon
{20} Icosagon
{5/2} Pentagram
{6/2} Hexagram
{8/2} Octagram
{8/3} Octagram
{10/2} Decagram
{10/3} Decagram
{12/2}  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
7 7 9 9 8 11 10 13 1 1211 21


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
6 9 12 12 14 21 12


Triangle — Decagon (7 pieces)


Square — Decagon (7 pieces)


Pentagon — Decagon (9 pieces)


Hexagon — Decagon (9 pieces)

Hexagon — Decagon (8 pieces with 3 turned over)


Heptagon — Decagon (11 pieces)


Octagon — Decagon (10 pieces)


Enneagon — Decagon (13 pieces)


Decagon — Dodecagon (12 pieces)

Decagon — Dodecagon (11 pieces with 2 turned over)


Decagon — Icosagon {20} (21 pieces)


Decagon — Pentagram (6 pieces)

Discovered by Harry Lindgren (1964).


Decagon — Hexagram (9 pieces)


Decagon — Octagram {8/2} (12 pieces)

The two overlay diagrams show the decagon strip before and after modification. The first overlay diagram results in a 14 piece dissection: the fourteenth piece is a tiny piece at the bottom left of the overlay parallelogram. The modification results in a saving of two pieces. Usually such a modification only saves a single piece.


Decagon — Octagram {8/3} (12 pieces)


Decagon — Decagram {10/2} (14 pieces)


Decagon — Decagram {10/3} (21 pieces)


Decagon — Dodecagram {12/2} (12 pieces)


Decagon — Silver Rectangle (7 pieces)


Decagon — Golden Rectangle (6 pieces)


Decagon — Domino (7 pieces)


Decagon — Optimised Rectangle (4 pieces)


Decagon — Greek Cross (10 pieces)


Decagon — Latin Cross (10 pieces)

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