Three Way Dissections
There is a very large number of possible three way dissections that can be
performed. To limit this number I have restricted myself to looking for three
way dissections of the regular polygons and polygrams that can be solved in
twelve or fewer pieces.
Triangle — Square — Pentagon (10 pieces)
Triangle — Square — Hexagon (9 pieces)
Discovered by Harry Lindgren.
Triangle — Square — Octagon (11 pieces)
Triangle — Square — Dodecagon (11 pieces)
Triangle — Square — Pentagram (12 pieces)
Triangle — Square — Hexagram (8 pieces)
The dissection is hingeable.
Triangle — Square — Octagram {8/2} (12 pieces)
Triangle — Square — Dodecagram {12/2} (11 pieces)
Triangle — Pentagon — Hexagon (12 pieces)
Triangle — Pentagon — Hexagram (11 pieces)
Triangle — Hexagon — Octagon (12 pieces)
Triangle — Hexagon — Dodecagon (11 pieces)
Triangle — Hexagon — Hexagram (11 pieces)
Triangle — Heptagon — Hexagram (12 pieces)
There is a small twelfth piece that can just be seen at the
centre of the hexagram. I have not yet found a way to remove this blemish.
Triangle — Octagon — Hexagram (11 pieces)
Triangle — Hexagram — Dodecagram {12/2} (11 pieces)
Square — Pentagon — Hexagon (12 pieces)
Square — Pentagon — Hexagon (11 pieces with 2 turned over)
Square — Pentagon — Octagon (12 pieces)
Square — Pentagon — Octagon (11 pieces with 1 turned over)
Square — Pentagon — Dodecagon (12 pieces)
There is a small thin twelfth piece that can just be seen at the top left of the
dodecagon.
Square — Pentagon — Hexagram (12 pieces)
Square — Hexagon — Heptagon (12 pieces)
Square — Hexagon — Octagon (11 pieces)
Square — Hexagon — Octagon (10 pieces with 2 turned over)
Square — Hexagon — Dodecagon (11 pieces)
Square — Hexagon — Hexagram (10 pieces)
The dissection is translational.
Square — Octagon — Dodecagon (11 pieces)
Square — Octagon — Hexagram (11 pieces)
Square — Dodecagon — Hexagram (12 pieces)
Hexagon — Dodecagon — Hexagram (12 pieces)