You can arrange them to make a cube.
12 edges, 6 faces.
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Take two toothpicks that create an outside corner. Cross them like a + inside one of the remaining boxes. Count the new four smaller boxes inside it as 4, the one they are formed in as 5, and the two untouched boxes as 6 and 7. (The trick is to remember to count the larger box the 4 are formed in.)
Fuor toothpicks from 16 leave 12 which, by coincidence (?) is exactly enough for four equilateral triangles!
If they are 1 x 1 squares there would be 144 in a 12 x 12 grid.
608
6 triangles is 18 and 3 squares is 12 18 +12 ------- 30