Octagon Dissections

Author : Gavin Theobald

Triangle — Octagon (7 pieces)

Previously Harry Lindgren had discovered an 8 piece solution.

Both of these are TT2 dissections.

Square — Octagon (5 pieces)

This dissection uses the method of completed tessellations. This dissects a square with a small square to an octagon with the same small square.

This dissection first appeared in the circa 1300 anonymous Persian manuscript “Interlocks of Similar or Complementary Figures”.

Pentagon — Octagon (9 pieces)

Previously, Harry Lindgren found a different solution.

This is a PP dissection.

Pentagon — Octagon (8 pieces with 1 turned over)

This uses an octagon tessellation formed from strips.

Hexagon — Octagon (8 pieces)

Previously Harry Lindgren discovered a 9 piece solution. He would be annoyed with himself for missing the first of these two solutions.

The first solution is a PP dissection using a hexagon strip from a tessellation. The second solution is a TT2 dissection.

Hexagon — Octagon (7 pieces with 2 turned over)

This dissection uses the method of overlaid tessellations with both tessellations formed from strips.

Heptagon — Octagon (11 pieces)

Previously Harry Lindgren discovered an 13 piece solution.

This is a PP dissection.

Heptagon — Octagon (10 pieces with 1 turned over)

This dissection overlays a heptagon strip over an octagon tessellation formed from strips.

Octagon — Enneagon (12 pieces)

This dissection overlays a variable enneagon strip over an octagon tessellation formed from strips.

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.

Octagon — Hendecagon (16 pieces)
Octagon — Hendecagon (15 pieces with 1 turned over)

This dissection uses the TT2 method twice.

Octagon — Dodecagon (10 pieces)

This is a PP dissection.

Octagon — Hexadecagon (17 pieces)

The basic method used by this dissection was discovered by Greg Frederickson but required turning over 8 pieces. I introduced the curved cuts to avoid this. The method works for all {n} to {2n} dissections.

Octagon — Pentagram (10 pieces)

This dissection uses the TT2 method twice.

Octagon — Hexagram (8 pieces)

Previously Harry Lindgren discovered a 9 piece solution.

This is a PP dissection.

Octagon — Octagram {8/2} (11 pieces)

This dissectio uses the method of completed tessellations. This dissects an octagon and a small square to an octagram with the same small square.

Octagon — Octagram {8/3} (6 pieces)

Discovered by Harry Lindgren.

Octagon — Decagram {10/2} (13 pieces)
Octagon — Decagram {10/2} (12 pieces with 1 turned over)

This is a PP dissection. By combining decagram strips, a decagram tessellation is formed that saves a piece.

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

See this page for an explanation of the method used.

Octagon — Dodecagram {12/3} (12 pieces)

Octagon — Hexadecagram {16/2} (16 pieces with 4 turned over)

Discovered by Greg Frederickson.

Octagon — Silver Rectangle (4 pieces)

Octagon — Golden Rectangle (6 pieces)

Previously Harry Lindgren also discovered a 6 piece solutions, but used a different octagon strip.

This is a PP dissection.

Octagon — Domino (6 pieces)

This is a PP dissection.

Octagon — Optimised Rectangle (4 pieces)

Octagon — Greek Cross (8 pieces)

Previously Harry Lindgren found two different 9 piece solutions.

My first solution uses the method of overlaid tessellations. The second solution uses the method of TT2 dissection.

Octagon — Latin Cross (8 pieces)

Previously Harry Lindgren found a different 8 piece solution.

This dissection uses the TT2 method.