Decagon Dissections

Author : Gavin Theobald

Triangle — Decagon (7 pieces)

Previously Ernest Irving Freese discovered a 10 piece solution and later Harry Lindgren discovered first a 9 piece and then 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)

Previously, Harry Lindgren found first an 11 piece and then a 10 piece solution.

I very nearly missed finding this PT dissection. The *red* piece is so nearly cut into two, adding another two pieces to this dissection, that I did not think that it was possible. Fortunately I checked and hence obtained another record.

Hexagon — Decagon (9 pieces)

Previously Harry Lindgren discovered a different 9 piece solution.

This is a PP dissection.

Hexagon — Decagon (8 pieces with 3 turned over)

This dissection overlays a decagon strip over a hexagon tessellation formed from strips.

Heptagon — Decagon (11 pieces)

Previously Harry Lindgren discovered an 13 piece solution.

This is a PP dissection.

Octagon — Decagon (10 pieces)

Previously Harry Lindgren discovered two different 12 piece solutions.

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

Enneagon — Decagon (13 pieces)

This is a PP dissection.

Decagon — Dodecagon (12 pieces)

This is a PP dissection. 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)

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

Decagon — Icosagon {20} (21 pieces)

The basic method used by this dissection was discovered by Greg Frederickson but required turning over 20 pieces. I introduced the curved cuts to avoid this. The method works for all {n} to {2n} dissections.

Decagon — Pentagram (6 pieces)

Discovered by Harry Lindgren.

Decagon — Hexagram (9 pieces)

Previously Harry Lindgren discovered a different 9 piece solution.

This is a PP dissection.

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)

This is a PP dissection.

Decagon — Decagram {10/2} (14 pieces)

This is a PP dissection.

Decagon — Decagram {10/3} (21 pieces)

The basic method used by this dissection was discovered by Greg Frederickson but required turning over 10 pieces. I introduced the curved cuts to avoid this. The method works for many {p} to {p/q} dissections.

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

See this page for an explanation of the method used.

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)

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

Decagon — Golden Rectangle (6 pieces)

Previously Harry Lindgren discovered a 7 piece solution.

This is a PP dissection.

Decagon — Domino (7 pieces)

This is a PP dissection. 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)

Previously Harry Lindgren discovered a different 10 piece solution.

This is a TT2 dissection.

Decagon — Latin Cross (10 pieces)

Previously Harry Lindgren discovered a different 10 piece solution.

This is a TT2 dissection. The two overlays show the strips before and after the modification of the decagon strip that saves a piece.