Decagon Dissections

Author : Gavin Theobald

{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
{R_ϕ}	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	9⁸	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

Triangle — Decagon (7 pieces)

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

I’m very pleased with this dissection. It’s one of only two dissections in which I use this particular decagon strip.

Square — Decagon (7 pieces)

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

Pentagon — Decagon (9 pieces)

Hexagon — Decagon (9 pieces)

Hexagon — Decagon (8 pieces with 3 turned over)

Heptagon — Decagon (11 pieces)

Octagon — Decagon (10 pieces)

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

Enneagon — Decagon (13 pieces)

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.

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)

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

Decagon — Golden Rectangle (6 pieces)

Decagon — Domino (7 pieces)

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

Decagon — Optimised Rectangle (4 pieces)

Decagon — Greek Cross (10 pieces)

Decagon — Latin Cross (10 pieces)

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

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