The Bridged Tritan are polyforms of three rectangular and isosceles triangles where vertex connections are also allowed. The vertex connections must not overlap but may share a vertex node. This procedure generates a tile set of 74 figures, but two of them have a completely surrounded hole and are put aside. The remaining 72 figures can fill various forms. The relatively large number of tiles needs hours or days of computing time to find solutions.
To compute solutions of Bridged TriTan with the Logelium method, special care is needed for modelling the connection nodes. Each node consists of nine atoms which connect the triangles in a way that bridges are allowed but no overlaps can occur. The following picture shows an example of a connection node with three concurrent tiles and two more attaching tiles.
We connect the triangles with circle sections to get an elegant shape for the pieces. The triangles then are nicely bridged and can be build physically.
It is rather difficult to make the pieces by hand, because they need to fit exactly to look really good. So I let a company manufacture a set of laser cut pieces from 6mm acrylic. This worked out very fine.
Besides the diagonal rectangle TB3_D9x6 there are some more rectangle solutions.
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rectangle of 27x4 squares rectangle of 9x12 squares
rectangle of 6x18 squares
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There are 107 HexaTan figures, each consisting of six triangles. We can build six fold magnifications of HexaTans with the set of 72 Bridged TriTans.
A solution was found for this completely symmetrical form.
