Square to Polygram Dissections

Square — Pentagram (7 pieces)

This is a TT2 dissection.

Square — Hexagram (5 pieces)

This PP dissection is translational.

Discovered by Harry Bradley (1921).

Square — Heptagram {7/2} (10 pieces)

Square — Heptagram {7/3} (12 pieces)

This dissection uses the TT2 method twice. There is the main heptagram strip and also a narrow strip of triangles. Since both strips repeat at the same rate they can be overlaid side by side.

Square — Octagram {8/2} (7 pieces)

Published by Greg Frederickson (1997).

Square — Octagram {8/3} (8 pieces)

There are many different ways to solve this dissection in 8 pieces, but I have been unable to find a seven piece solution.

Square — Enneagram {9/2} (11 pieces)
Square — Enneagram {9/2} (10 pieces with 1 turned over)

These are PP dissections.

Square — Enneagram {9/3} (13 pieces)

This is a PP dissection.

Square — Enneagram {9/3} (12 pieces with 3 turned over)

This is a PP dissection.

Square — Enneagram {9/4} (19 pieces with 3 turned over)

This is a PP dissection.

Square — Decagram {10/2} (10 pieces)

This is a PP dissection.

Square — Decagram {10/2} (9 pieces with 1 turned over)

Square — Decagram {10/3} (11 pieces)

This is a PP dissection.

Square — Decagram {10/3} (10 pieces with 4 turned over)

This is a PP dissection.

Anton Hanegraaf was the first to discover a 10 piece solution.

This is a PP dissection.

Square — Decagram {10/4} (10 pieces)

This is a PP2 dissection.

Square — Dodecagram {12/2} (8 pieces)

Note that there are some very short edges that are not visible in these views. Click on the images to see enlarged versions.

Rectangle {R_1.05} — Dodecagram {12/2} (8 pieces)

These diagrams use the same technique as for the square, but better show the way in which the dissection works. Click on the images to see enlarged versions.

Square — Dodecagram {12/3} (8 pieces)

This dissection uses the method of overlaid tessellations.

Square — Dodecagram {12/4} (11 pieces)

Discovered by Greg Frederickson (1997).

This dissection is a clever use of the method of completed tessellations.

Square — Dodecagram {12/5} (9 pieces)

Discovered by Greg Frederickson (1972).

Square — Hexadecagram {16/2} (13 pieces)

Square — Hexadecagram {16/2} (12 pieces with 2 turned over)

Square — Icositetragram {24/2} (15 pieces with 1 turned over)