More Square Dissections

Author : Gavin Theobald

{4} Rotated Square
{6} Rotated Hexagon
{R√2} Silver Rectangle
{Rϕ} Golden Rectangle
{R2} Domino
{G} Greek Cross
{L} Latin Cross
{M} Maltese Cross


Square — Square rotated by 15° (5 pieces)
Square — Square rotated by 30° (5 pieces)
Square — Square rotated by 45° (5 pieces)

The dissection is translational or hingeable.

Obviously, this dissection could be performed without any dissection at all, but the challenge here is to perform the dissection using only translation without any rotation of any of the pieces. The dissection works for a range of angles up to a rotation of over 50°.

Interestingly, the rotated square is just the unrotated square mirrored along the long diagonal of the kite shaped piece. The dissection can be greatly varied but this version only has three different shaped pieces and hence has much greater symmetry.

I am grateful to Misty Cremo for making me aware of this problem.


Square — Hexagon rotated by 5° (6 pieces)
Square — Hexagon rotated by 10° (6 pieces)
Square — Hexagon rotated by 15° (6 pieces)

These dissections are translational.

As for the square dissections above, the challenge here is to perform the dissection using only translation without any rotation of any of the pieces. The dissection works for a range of angles up to a rotation of over 20°. The range is sufficient to allow rotation to any angle.


Square — Silver Rectangle (3 pieces)

The dissection is translational.


Square — Golden Rectangle (3 pieces)

The dissection is translational.


Square — Domino (3 pieces)

The dissection is translational and hingeable.


Square — Greek Cross (4 pieces)

The dissection is translational and hingeable. This dissection uses the method of overlaid tessellations.

Described by Don Lemon.


Square — Latin Cross (5 pieces)

Harry Lindgren solved this in 5 pieces using a PP dissection.

This dissection uses the method of completed tessellations. It dissects four squares and a small square to four latin crosses and the same small square. To avoid turning over one of the pieces, that piece is altered to have a curved edge. There are much simpler versions of this dissection, but this one demonstrates some unusual techniques.


Square — Maltese Cross (7 pieces)

Discovered by A. E. Hill (1926).