# Bridged Polyiamonds

2018/02/19

Equilateral triangles joined at their sides are called Polyiamonds. If connection at the corners are also allowed we have pseudo Polyiamonds. To get real pieces the connection between the corners must be made by little bridges and the other corners must be rounded to allow the bridges to pass between them. Therefore these pieces are called bridged or rounded polyiamonds.
If all touching corners were bridged, we would get too many pieces with holes. Therefore it seems to be better to remove unneccessary bridges. From the pseudo tetriamond in the picture you can derive two two-sided bridged tetriamonds and four one-sided bridged tetriamonds.

The left bridges must produce a spanning tree with ordinary polyiamonds as vertices. In the example the vertices are single triangles.
I learned about the concept from the Logelium site more than a decade ago and wrote a program to construct figures with the pieces. SVG-files for the shapes were also provided by the program and I used them to order laser cut bridged triamonds from 6mm acrylics. After this I found a symmetric construction with the bridged tetriamonds shown below but laser cutting of all these pieces seemed to be too expensive at that time and therefore I stopped searching for further constructions.
After I had bought a 3d-printer kit it was cheap to produce such pieces and I decided to let the computer search for new constructions. Click the sets to see them.

Set Number of Triangles Number of Pieces Total Volume
Bridged Triamonds
(two-sided)
3 11 33
Bridged Triamonds
(one-sided)
3 16 48
Bridged Triamonds & Diamonds
(two-sided)
2..3 14 39
Bridged Triamonds & Diamonds
(one-sided)
2..3 19 54
Bridged Tetriamonds
(two-sided)
4 82 328
Bridged Tetriamonds
(one-sided)
4 143 572
Bridged Triamonds & Tetriamonds
(two-sided)
3..4 93 361

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