Octagram {8/2} 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
{8/3} 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
9 7 11 9 12 11 15 12 9


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 1 13 1614 13 13

Triangle — Octagram (9 pieces)

This is a PP dissection.

Square — Octagram (7 pieces)

Harry Lindgren found an 8 piece solution, but Greg Frederickson found this improved solution.

Pentagon — Octagram (11 pieces)

Hexagon — Octagram (9 pieces)

Heptagon — Octagram (12 pieces)

Octagon — Octagram (11 pieces)

Enneagon — Octagram (15 pieces)

Decagon — Octagram (12 pieces)

The two overlay diagrams show the decagon strip before and after modification. The first overlay diagram results in a 14 piece dissection: the fourteenth piece is a tiny piece at the bottom left of the overlay parallelogram. The modification results in a saving of two pieces. Usually such a modification only saves a single piece.

Dodecagon — Octagram (9 pieces)

Pentagram — Octagram (13 pieces)

Hexagram — Octagram (10 pieces)

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

Octagram — Decagram {10/2} (16 pieces)

Octagram — Decagram {10/2} (14 pieces with 1 turned over)

Octagram — Dodecagram {12/2} (13 pieces)

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

Silver Rectangle — Octagram (8 pieces)

Golden Rectangle — Octagram (8 pieces)

Domino — Octagram (7 pieces)
Optimised Rectangle — Octagram (7 pieces)
Domino — Octagram (6 pieces with 2 turned over)
Optimised Rectangle — Octagram (6 pieces with 2 turned over)

Greek Cross — Octagram (7 pieces)

Latin Cross — Octagram (10 pieces)