Heptagon Dissections

Author : Gavin Theobald

The majority of the dissections of this page are due to the discovery of a single P strip.

Triangle — Heptagon (8 pieces)

Previously Harry Lindgren had discovered a 9 piece solution.

This is a PP dissection.

Square — Heptagon (7 pieces)

As described by Greg Frederickson, this was first dissected in 10 pieces by George Wotherspoon, then dissected in 9 pieces by Crofton Edward Pym Sankey and H. G. Charlton, then in 8 pieces by Anton Hanegraaf.

This was one of the first dissection improvements I found, and I am particularly proud of finding it. The previous record that I knew of was a 9 piece dissection found by Harry Lindgren. I managed to improve this to 8 pieces in a number of ways, and this made me sure that there had to be a 7 piece solution. The problem is the plain square strip cannot be overlaid over the usual heptagon strip since the square strip is too wide. So I looked for a narrower heptagon strip. The method I use allows me to produce a range of heptagon strips (so this is an example of a variable strip), but I chose the one that ensures that an edge of the heptagon coincides with an edge of the square. This saves a piece giving a 7 piece record. I do not believe that a further improvement exists.

Pentagon — Heptagon (9 pieces)

Previously, Harry Lindgren found an 11 piece solution.

This is a PP dissection.

Hexagon — Heptagon (8 pieces)

Previously Harry Lindgren discovered an 11 piece solution.

This is a PP dissection.

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.

Heptagon — Enneagon (13 pieces)

This dissection uses the method of variable tessellation.

Heptagon — Decagon (11 pieces)

Previously Harry Lindgren discovered an 13 piece solution.

This is a PP dissection.

Heptagon — Hendecagon (15 pieces)

This dissection uses the TT2 method twice.

Heptagon — Dodecagon (11 pieces)

This is a PP dissection.

Heptagon — Tetradecagon (15 pieces)

The basic method used by this dissection was discovered by Greg Frederickson but required turning over 7 pieces. I introduced the curved cuts to avoid this. The method works for all {n} to {2n} dissections.

Heptagon — Pentagram (11 pieces)

This is a TT2 dissection.

Heptagon — Hexagram (9 pieces)

Previously Harry Lindgren discovered an 11 piece solution.

This is a PP dissection.

Heptagon — Heptagram {7/2} (15 pieces)

The basic method used by this dissection was discovered by Greg Frederickson but required turning over 7 pieces. I introduced the curved cuts to avoid this. The method works for many {p} to {p/q} dissections.

Heptagon — Heptagram {7/3} (13 pieces)

Greg Frederickson found a 14 piece solution, but Anton Hanegraaf found a minor modification to reduce this to 13 pieces.

Heptagon — Octagram {8/2} (12 pieces)

Heptagon — Octagram {8/3} (12 pieces)

This is a PP dissection.

Heptagon — Decagram {10/2} (14 pieces)

This is a PP dissection.

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

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

Heptagon — Dodecagram {12/2} (11 pieces)

See this page for an explanation of the method used.

Heptagon — Dodecagram {12/3} (13 pieces)

Heptagon — Tetradecagram {14/2} (12 pieces)

This is a modification of a dissection found by Greg Frederickson. My variation is more symmetric, but uses the same number of pieces. In Frederickson’s first book he mentions an 11 piece version of this dissection, but he has not been able to find a copy of it. Either he miscounted the number of pieces, or there is a forgotten trick to save a piece. So, can you improve this dissection?

Heptagon — Silver Rectangle (7 pieces)

This is a PP dissection.

Heptagon — Golden Rectangle (7 pieces)

Previously Harry Lindgren discovered a 9 piece solution.

This is a PP dissection.

Heptagon — Domino (7 pieces)

This is a PP dissection.

Heptagon — Optimised Rectangle (5 pieces)

Heptagon — Greek Cross (9 pieces)

Previously Harry Lindgren discovered a 12 piece solution.

This is a PP dissection.

Heptagon — Latin Cross (8 pieces)

Previously Harry Lindgren discovered a 12 piece solution.

This is a PP dissection.