Optimised Rectangle Dissections
The optimised rectangle {R×} is a rectangle of whatever proportions that gives
the best dissection for a particular polygon. It is not necessarily the optimal rectangle as a
better dissection may one day be found.
|
|
|
| 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 |
| 5
| 4
| 8
|
| 7 6
| 4
| 10
| 10 9
| 15
| 8
| 8 7
| 6
| 7
| 8
|
| 7
|
|
Triangle — Optimised Rectangle (3 pieces)
Triangle — Optimised Rectangle (2 pieces with 1 turned over)
The first dissection is hingeable.
Pentagon — Optimised Rectangle (4 pieces)
Hexagon — Optimised Rectangle (3 pieces)
The dissection is translational. Each piece has the same area.
Heptagon — Optimised Rectangle (5 pieces)
Octagon — Optimised Rectangle (4 pieces)
Enneagon — Optimised Rectangle (7 pieces)
Decagon — Optimised Rectangle (4 pieces)
Hendecagon — Optimised Rectangle (9 pieces)
Dodecagon — Optimised Rectangle (5 pieces)
Tridecagon — Optimised Rectangle (10 pieces)
Tetradecagon — Optimised Rectangle (7 pieces)
Pentadecagon — Optimised Rectangle (10 pieces)
Hexadecagon — Optimised Rectangle (9 pieces)
Octadecagon — Optimised Rectangle (9 pieces)
Optimised Rectangle — Pentagram (5 pieces)
Optimised Rectangle — Hexagram (4 pieces)
The dissection is translational.
Optimised Rectangle — Heptagram {7/2} (8 pieces)
Optimised Rectangle — Octagram {8/2} (7 pieces)
Optimised Rectangle — Octagram {8/2} (6 pieces with 2 turned over)
Optimised Rectangle — Octagram {8/3} (4 pieces)
Optimised Rectangle — Enneagram {9/3} (10 pieces)
Optimised Rectangle — Enneagram {9/3} (9 pieces with 2 turned over)
Optimised Rectangle — Decagram {10/2} (8 pieces)
Optimised Rectangle — Decagram {10/3} (8 pieces)
Optimised Rectangle — Decagram {10/3} (7 pieces with 1 turned over)
Optimised Rectangle — Decagram {10/4} (6 pieces)
Optimised Rectangle — Dodecagram {12/2} (7 pieces)
Optimised Rectangle — Dodecagram {12/5} (7 pieces)
Optimised Rectangle — Greek Cross (3 pieces)
The dissection is translational and hingeable.
Optimised Rectangle — Latin Cross (3 pieces)
The dissection is translational.