Triangle Dissections

Triangle — Square (4 pieces)

This TT2 dissection is hingeable.

The discovery of this dissection is normally attributed to Henry Ernest Dudeney (1902) but may have been first discovered by C. W. McElroy (1902).

Triangle — Pentagon (6 pieces)

Discovered by Harry Lindgren (1961).

This is a rare use of the TT1 technique.

Triangle — Pentagon (6 pieces)

This is perhaps not the best example of a dissection of triangle and pentagon, but it is new and it does demonstrate the TT22 technique.

Triangle — Hexagon (5 pieces)

Discovered by Harry Lindgren (1961).

This uses the TT2 technique. I know of no other 5 piece solution to this dissection.

Triangle — Heptagon (8 pieces)

Previously Harry Lindgren (1961) had discovered a 9 piece solution.

This is a PP dissection.

Triangle — Octagon (7 pieces)

Previously Harry Lindgren (1961) had discovered an 8 piece solution.

Both of these are TT2 dissections.

Triangle — Enneagon (8 pieces)

This dissection makes use of the TT2 technique.

Previously Freese found a 9 piece solution to this dissection. In Lindgren's book (1961) he states “The conclusion is that if you can beat Freese, you will have found a needle in a haystack”. I found the needle! This was one of the first dissection improvements that I found, and I am particularly pleased with it.

Triangle — Decagon (7 pieces)

Previously Harry Lindgren (1961) had discovered an 8 piece solution.

This is a TT2 dissection that uses a variable decagon strip. The two overlays show the strips before and after the modification of the decagon strip that saves a piece.

I’m very pleased with this dissection. It’s one of only two dissections in which I use this particular decagon strip.

Triangle — Hendecagon (11 pieces)

Reducing this dissection to 11 pieces was not easy. In the wider hendecagon strip the two large pieces can be varied in size. I vary the size to ensure that a hendecagon edge passes exactly through the intersection of triangle edges at the edge of the triangle strip. This saves a piece. The second overlay diagram shows the initial stage of overlaying the second two strips. I modify the shape of the trapezium of the thinner triangle strip to save a further two pieces.

Triangle — Dodecagon (8 pieces)

Previously Harry Lindgren (1961) had discovered a different 8 piece solution.

This is a PP dissection.

There are many 8 piece solutions to this dissection, so it’s disappointing that I’ve been unable to find anything better.

Triangle — Tridecagon (12 pieces)

Triangle — Tetradecagon (11 pieces)

Triangle — Hexadecagon (12 pieces)

Triangle — Icosagon (13 pieces)

Triangle — Pentagram (7 pieces)

Previously Harry Lindgren (1961) had discovered a 9 piece solution.

This uses the TT2 technique.

Triangle — Hexagram (5 pieces)

Discovered by Harry Lindgren (1961).

The dissection is hingeable.

Triangle — Heptagram {7/3} (12 pieces)

This dissection overlays the triangle T strip with two heptagram T strips.

Triangle — Octagram {8/2} (9 pieces)

This is a PP dissection.

Triangle — Octagram {8/3} (8 pieces)

This is a TT2 dissection that uses a variable octagram strip. The two overlays show the strips before and after the modification of the octagram strip that saves a piece.

Triangle — Decagram {10/2} (10 pieces)

This uses the TT2 technique.

Triangle — Decagram {10/4} (10 pieces)

This uses the PT technique.

Triangle — Dodecagram {12/2} (6 pieces)

Discovered by Harry Lindgren (1964).

Triangle — Silver Rectangle (4 pieces)

This uses the TT2 technique. The dissection is hingeable.

Triangle — Golden Rectangle (4 pieces)

This uses the TT2 technique. The dissection is hingeable.

Triangle — Domino (4 pieces)

This uses the PT technique. The dissection is hingeable.

Triangle — Optimised Rectangle (3 pieces)
Triangle — Optimised Rectangle (2 pieces with 1 turned over)

The first dissection is hingeable.

Triangle — Greek Cross (5 pieces)

This uses the TT2 technique.

Discovered by Harry Lindgren (1961).

Triangle — Latin Cross (5 pieces)

Previously Harry Lindgren (1961) discovered a different 5 piece solution.

This solution uses the TT2 technique.