Octagram {8/3} Dissections

Author : Gavin Theobald

{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{9} Enneagon
{10} Decagon
{12} Dodecagon
{5/2} Pentagram
{6/2} Hexagram
{8/2} Octagram
{10/2} Decagram
{12/2}  Dodecagram
{12/3}  Dodecagram
{R√2} Silver Rectangle
{Rϕ} Golden Rectangle
{R2} Domino
{R×} Optimised Rectangle
{G} Greek Cross
{L} Latin Cross
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
8 8 9 98 12 6 13 12 12


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
13 10 13 1 14 1413 14

Triangle — Octagram (8 pieces)

This is a TT2 dissection that uses a variable octagram strip. The two overlays show the strips before and after the modification of the octagram strip that saves a piece.

Square — Octagram {8/3} (8 pieces)

Harry Lindgren was the first to find an 8 piece dissection. There are many other ways to solve this dissection in 8 pieces. This suggests that a seven piece solution may exist, but if it does, I have been unable to find it.

The second dissection is a PP dissection. The strips’ anchor points are aligned for the sake of greater symmetry, but this is not necessary.

Pentagon — Octagram (9 pieces)

Hexagon — Octagram (9 pieces)

Hexagon — Octagram (8 pieces with 1 turned over)

Heptagon — Octagram (12 pieces)

Octagon — Octagram (6 pieces)

Discovered by Harry Lindgren.

Enneagram — Octagram (13 pieces)

Decagon — Octagram (12 pieces)

Dodecagon — Octagram (12 pieces)

Pentagram — Octagram (13 pieces)

The two overlays show the strips before and after the modification of the octagram strip that saves a piece.

Hexagram — Octagram (10 pieces)

The two overlays show the strips before and after the modification of the octagram strip that saves a piece.

Octagram {8/2} — Octagram {8/3} (13 pieces)

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

Octagram — Dodecagram {12/2} (14 pieces)

Octagram — Dodecagram {12/2} (13 pieces with 1 turned over)

Octagram — Dodecagram {12/3} (14 pieces)

Silver Rectangle — Octagram (5 pieces)

Golden Rectangle — Octagram (7 pieces)

The two overlays show the strips before and after the modification of the octagram strip that saves a piece.

Domino — Octagram (7 pieces)

The two overlays show the strips before and after the modification of the octagram strip that saves a piece.

Optimised Rectangle — Octagram (4 pieces)

Greek Cross — Octagram (10 pieces)

Latin Cross — Octagram (11 pieces)

The two overlays show the strips before and after the modification of the octagram strip. This saves a piece.