Triangle - 2 × Triangle (5 pieces)
Square - 2 × Square (4 pieces)
Pentagon - 2 × Pentagon (9 pieces)
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 × Heptagon (10 pieces with 1 turned over)
Discovered by Greg Frederickson (1997).
Octagon - 2 × Octagon (8 pieces)
Enneagon - 2 × Enneagon (19 pieces)
Discovered by Harry Hart (1877). This is a modification discovered by Ernest Irving Freese (1957).
Enneagon - 2 × Enneagon (16 pieces with 3 turned over)
Discovered by Greg Frederickson.
Decagon - 2 × Decagon (16 pieces)
Hendecagon - 2 × Hendecagon (23 pieces)
Discovered by Harry Hart (1877). This is a modification discovered by Ernest Irving Freese (1957).
Dodecagon - 2 × Dodecagon (10 pieces)
Tridecagon - 2 × Tridecagon (21 pieces with 6 turned over)
Discovered by Greg Frederickson.
Tetradecagon - 2 × Tetradecagon (22 pieces with 7 turned over)
Discovered by Greg Frederickson.
Pentadecagon - 2 × Pentadecagon (24 pieces with 7 turned over)
Discovered by Greg Frederickson.
Hexadecagon - 2 × Hexadecagon (16 pieces)
Discovered by Greg Frederickson (1972).
Hexagram - 2 × Hexagram (11 pieces)
First discovered by Anton Hanegraaf (before 1990).
Octagram - 2 × Octagram (11 pieces)
Discovered by Harry Lindgren (1964).
Octagram - 2 × Octagram (12 pieces)
Discovered by Harry Lindgren (1964).
Dodecagram - 2 × Dodecagram (13 pieces)
Discovered by Greg Frederickson (1972).
Dodecagram - 2 × Dodecagram (12 pieces)
Discovered by Greg Frederickson (1972).
Dodecagram - 2 × Dodecagram (18 pieces)
Discovered by Greg Frederickson (1974).
Golden Rectangle - 2 × Golden Rectangle (5 pieces)
Greek Cross - 2 × Greek Cross (5 pieces)
