Locked Octagon Dissections

Author : Gavin Theobald

The small figures in the table above indicate the overhead compared to an ordinary dissection. They give an indication of where improvement may be possible. Is it possible to reduce this overhead to zero?

Triangle = Octagon (10 pieces with 3 turned over)

This dissection is based around the first one here.

Square = Octagon (8 pieces with 3 turned over)

The unlocked version of this dissection is here. The twist hinged version of this dissection requires an extra piece. Here, the central square is held in place by the surrounding pieces.

Pentagon = Octagon (11 pieces with 4 turned over)

Hexagon = Octagon (10 pieces with 5 turned over)

I am pleased with this dissection. It was not very easy to find.

Note that the diagram show the dissection with six pieces turned over, but by simply replacing one of the polygons with its mirror image reduces this to four pieces.

Octagon = Decagon (11 pieces with 4 turned over)

Many of the lugs of this dissection are too small. There are 6 small lugs visible, but actually there are another 4 that are the tenth of the size of these ones. Only at maximum zoom do they become visible.

Octagon = Decagon (12 pieces with 5 turned over)

This dissection removes the minute lugs of the previous dissection, but at the cost of an extra piece. Many of the lugs of this dissection are still too small, but I have not yet found a way to remove this imperfection.