Stacked Polytans


Polytans are built by connecting rectangular isosceles triangles at their short or long sides called s-sides or h-sides. Real pieces with a thickness greater than zero can be expanded by putting another triangle on top of them and this way you get the Stacked Polytans. The triangle must touch another triangle or square with its whole area and must be aligned to the grid. In the new layer you can add further triangles as usual.

According to these rules the red pieces are not included, because there are no matching triangles in the first and second layer. The green ones are correct examples, because there is a connection between a square and a triangle and the square is connected with another triangle.
I counted the pieces with a fixed number of triangles and got the following table

Number of Triangles 1 2 3 4 5 6 3 or 4
Number of Pieces 1 4 10 66 377 2762 76
Total Number of Triangles 1 8 30 264 1885 16572 294

After I had created the pieces I tried to make some constructions with the Tritans, the Tetratans and the combined set of Tritans and Tetratans.
At last I glued a Tetratan set of plastic triangles. Because the triangles were too thick I sawed and glued another set of Tritans and Tetratans made of wood.