This page contains a gallery of symmetric forms that you can make of the 16 onesided Bridged Triamonds. Ed Pegg gave me a hint to try the onesided version. Different from the twosided version there are hexagon symmetric forms possible.
135 * 12 solutions

1586 * 12 solutions

no solution

2706 * 12 solutions

175 * 12 solutions

6279 * 12 solutions

3681 * 12 solutions

67 * 12 solutions

1810 * 12 solutions

36 * 12 solutions

58 * 12 solutions

13117 * 6 solutions

27695 * 6 solutions

237 * 6 solutions

677 * 6 solutions

196 * 6 solutions

1124 * 6 solutions

9018 * 6 solutions

160551 * 6 solutions

390 * 3 solutions

45920 * 3 solutions

205 * 3 solutions

67411 * 2 solutions

87 * 4 solutions

75 * 4 solutions
