Square to Polygram Dissections

Author : Gavin Theobald

Home Index Square — {m/n} Contact  Colour
{5/2} Pentagram
{6/2} Hexagram
{7/2} Heptagram
{7/3} Heptagram
{8/2} Octagram
{8/3} Octagram
{9/2} Enneagram
{9/3} Enneagram
{9/4} Enneagram
{10/2} Decagram
{10/3} Decagram
{10/4} Decagram
{12/2} Dodecagram
{12/3} Dodecagram
{12/4} Dodecagram
{12/5}  Dodecagram
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
7 5 10 12 7 8 1110 1312 19 10 9 1110 10 8 8 11 9


Square — Pentagram (7 pieces)


Square — Hexagram (5 pieces)

Discovered by Harry Bradley (1921).

The dissection is translational.


Square — Heptagram {7/2} (10 pieces)


Square — Heptagram {7/3} (12 pieces)


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)


Square — Enneagram {9/3} (13 pieces)

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


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


Square — Decagram {10/2} (10 pieces)

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


Square — Decagram {10/3} (11 pieces)

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


Square — Decagram {10/4} (10 pieces)

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


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 {R1.05} — 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)


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

Discovered by Greg Frederickson (1997).


Square — Dodecagram {12/5} (9 pieces)

Discovered by Greg Frederickson (1972).

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