There are 10 two-sided bridged ditans with a total of 20 triangles. The SVG-file to cut or print
the pieces is here. Five of the ten pieces are balanced
under checkerboard coloring and so the numbers of all white and all black triangles are odd and different.
Therefore symmetric constructions with the whole set aren't possible.
Using only 9 pieces you can get for example a 3x3 square.
This can be regarded as a
3-fold replica of the square piece. 3-fold replicas of the following pieces are also possible. Click the
picture to see the solutions.
You can also replicate some polyominoes with a factor of sqrt(2). For the S,T or L tetrominoes you need 8 pieces,
for the V and I trominoes 6 pieces and for the domino 4 pieces.
Using the whole set you can at least get figures with only one reentrant angle.
Here are the 15 pieces laser cut from acrylic. At the back side there are little magnets to stick the
pieces on iron boards. Under checkerboard coloring there are 8 balanced pieces and we
can construct a lot of symmetric figures.
Two axes of symmetry:
Beside the X-shape in the title we can get a rectangle, a hexagon and an octagon.
Symmetry under 90 degree rotation:
Symmetry under 180 degree rotation:
One axis of symmetry:
What about figures with holes?
A 4x4 square with an 1x1 hole is a similar hole figure which can be made. Instead of the 1x1 square
hole we can also choose a hole
shaped like a ditan, if its triangles are same colord under checkerboard coloring and the slopes
of the hypotenuses are equal.
I also found a rectangle and a hexagon with an 1x1 hole or with a hole shaped like an hourglass.