Dissection of two polygons to one

Author : Gavin Theobald

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{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{9} Enneagon
{10} Decagon
{11} Hendecagon
{12} Dodecagon
{13} Tridecagon
{14} Tetradecagon
{15} Pentadecagon
{16} Hexadecagon
{6/2} Hexagram
{8/2} Octagram
{8/3} Octagram
{12/2}  Dodecagram
{12/3}  Dodecagram
{12/4}  Dodecagram
{R√2} Silver Rectangle
{Rϕ} Golden Rectangle
{R2} Domino
{G} Greek Cross
{L} Latin Cross
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5 4 9 8 10 8 1916 16 23 10 21 22 24 16


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
11 11 12 13 12 18


Triangle - 2 x Triangle

Triangle — 2 × Triangle (5 pieces)

Discovered by Harry Bradley (1930).
Square - 2 x Square

Square — 2 × Square (4 pieces)

The dissection is translational and hingeable.
Pentagon - 2 x Pentagon

Pentagon — 2 × Pentagon (9 pieces)


Hexagon - 2 x Hexagon

Hexagon — 2 × Hexagon (8 pieces with 3 turned over)

It is easy to change this so that only 2 pieces need be turned over.
Heptagon - 2 x Heptagon

Heptagon — 2 × Heptagon (10 pieces with 1 turned over)

Discovered by Greg Frederickson (1997).
Octagon - 2 x Octagon

Octagon — 2 × Octagon (8 pieces)


Enneagon - 2 x Enneagon

Enneagon — 2 × Enneagon (19 pieces)

Discovered by Harry Hart (1877). This is a modification discovered by Ernest Irving Freese (1957).

Enneagon - 2 x Enneagon

Enneagon — 2 × Enneagon (16 pieces with 3 turned over)

Discovered by Greg Frederickson.
Decagon - 2 x Decagon

Decagon — 2 × Decagon (16 pieces)


Hendecagon - 2 x Hendecagon

Hendecagon — 2 × Hendecagon (23 pieces)

Discovered by Harry Hart (1877). This is a modification discovered by Ernest Irving Freese (1957).
Dodecagon - 2 x Dodecagon

Dodecagon — 2 × Dodecagon (10 pieces)

Discovered by Harry Lindgren (1964).

The dissection is translational.
Tridecagon - 2 x Tridecagon

Tridecagon — 2 × Tridecagon (21 pieces with 6 turned over)

Discovered by Greg Frederickson.
Tetradecagon - 2 x Tetradecagon

Tetradecagon — 2 × Tetradecagon (22 pieces with 7 turned over)

Discovered by Greg Frederickson.
Pentadecagon - 2 x Pentadecagon

Pentadecagon — 2 × Pentadecagon (24 pieces with 7 turned over)

Discovered by Greg Frederickson.
Hexadecagon - 2 x Hexadecagon

Hexadecagon — 2 × Hexadecagon (16 pieces)

Discovered by Greg Frederickson (1972).
Hexagram - 2 x Hexagram

Hexagram — 2 × Hexagram (11 pieces)

First discovered by Anton Hanegraaf (before 1990).

The dissection is translational.
Octagram - 2 x Octagram

Octagram {8/2} — 2 × Octagram {8/2} (11 pieces)

Discovered by Harry Lindgren (1964).
Octagram - 2 x Octagram

Octagram {8/3} — 2 × Octagram {8/3} (12 pieces)

Discovered by Harry Lindgren (1964).
Dodecagram - 2 x Dodecagram

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

Discovered by Greg Frederickson (1972).

The dissection is translational.
Dodecagram - 2 x Dodecagram

Dodecagram {12/3} — 2 × Dodecagram {12/3} (12 pieces)

Discovered by Greg Frederickson (1972).

The dissection is translational.
Dodecagram - 2 x Dodecagram

Dodecagram {12/4} — 2 × Dodecagram {12/4} (18 pieces)

Discovered by Greg Frederickson (1974).

The dissection is translational.
Silver Rectangle - 2 x Silver Rectangle

Silver Rectangle — 2 × Silver Rectangle (2 pieces)

The dissection is translational.
Golden Rectangle - 2 x Golden Rectangle

Golden Rectangle — 2 × Golden Rectangle (5 pieces)

The dissection is translational.
Domino - 2 x Domino

Domino — 2 × Domino (5 pieces)

The dissection is translational.
Greek Cross - 2 x Greek Cross

Greek Cross — 2 × Greek Cross (5 pieces)

The dissection is translational and hingeable.
Latin Cross - 2 x Latin Cross

Latin Cross — 2 × Latin Cross (9 pieces)

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