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
{12/3}  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 14

Triangle — Decagon (7 pieces)

Previously Ernest Irving Freese discovered a 10 piece solution and later Harry Lindgren discovered an 8 piece solution.

This is a TT2 dissection that uses a variable decagon strip. The two overlays show the strips before and after the modification of the decagon strip that saves a piece. It is one of only two dissections in which I use this particular decagon strip.

I am very pleased with this dissection.

Square — Decagon (7 pieces)

Previously Ernest Irving Freese found an 8 piece solution to this dissection.

This is a PP dissection that uses a variable decagon strip. The two overlays show the strips before and after the modification of the decagon strip that saves a piece.

I like this dissection, although it has some odd shaped 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)

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.

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 — Dodecagram {12/3} (14 pieces)

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

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.