It's hard to find a set of horizontal and vertical spacings that produce a good fit. You can use Pythagoras' theorem to compute this exactly - but it's painful to search through all the possibilities looking for a good fit.

In many situations, you can tolerate a small error in the exact dimensions - and this makes it possible to find many horizontal and vertical combinations that come close enough to an exact fit to be useful.

I have only listed combinations that result in a diagonal beam length less than 15 studs because the longest Technic beams are 16 studs - which have only 15 holes.

3 studs x 10 plates = 5 studs exactly 6 studs x 20 plates = 10 studs exactly 8 studs x 15 plates = 10 studs exactly 9 studs x 30 plates = 15 studs exactly

This table lists all the combinations that are too loose ...these are sorted with the best fit first:

13 studs x 13 plates = 14.001 studs 11 studs x 12 plates = 12.002 studs 3 studs x 13 plates = 6.003 studs 15 studs x 1 plates = 15.005 studs 13 studs x 1 plates = 13.006 studs 14 studs x 1 plates = 14.006 studs 6 studs x 26 plates = 12.007 studs 11 studs x 1 plates = 11.007 studs 12 studs x 1 plates = 12.007 studs 10 studs x 1 plates = 10.008 studs 9 studs x 1 plates = 9.009 studs

8 studs x 1 plates = 8.010 studs 7 studs x 1 plates = 7.011 studs 6 studs x 1 plates = 6.013 studs 10 studs x 28 plates = 15.015 studs 5 studs x 1 plates = 5.016 studs 9 studs x 11 plates = 10.018 studs

4 studs x 1 plates = 4.020 studs 15 studs x 2 plates = 15.021 studs 14 studs x 2 plates = 14.023 studs 2 studs x 22 plates = 9.024 studs 13 studs x 2 plates = 13.025 studs 3 studs x 1 plates = 3.027 studs 12 studs x 2 plates = 12.027 studs 11 studs x 2 plates = 11.029 studs 4 studs x 23 plates = 10.032 studs 10 studs x 2 plates = 10.032 studs 8 studs x 19 plates = 11.034 studs 9 studs x 2 plates = 9.035 studs 2 studs x 1 plates = 2.040 studs 8 studs x 2 plates = 8.040 studs 7 studs x 18 plates = 10.042 studs 9 studs x 20 plates = 12.042 studs 9 studs x 16 plates = 11.044 studs 7 studs x 2 plates = 7.046 studs 15 studs x 3 plates = 15.048 studs

1 studs x 25 plates = 10.050 studs 14 studs x 3 plates = 14.051 studs 6 studs x 2 plates = 6.053 studs 13 studs x 3 plates = 13.055 studs 3 studs x 24 plates = 10.058 studs 9 studs x 27 plates = 14.058 studs 13 studs x 19 plates = 15.059 studs 6 studs x 29 plates = 13.060 studs 10 studs x 21 plates = 13.060 studs 12 studs x 3 plates = 12.060 studs 1 studs x 20 plates = 8.062 studs 7 studs x 10 plates = 8.062 studs 5 studs x 2 plates = 5.064 studs 11 studs x 3 plates = 11.065 studs 3 studs x 16 plates = 7.068 studs 6 studs x 17 plates = 9.069 studs 10 studs x 3 plates = 10.072 studs 12 studs x 13 plates = 13.078 studs 14 studs x 14 plates = 15.078 studs 4 studs x 2 plates = 4.079 studs 9 studs x 3 plates = 9.080 studs 1 studs x 15 plates = 6.083 studs 15 studs x 4 plates = 15.085 studs 11 studs x 22 plates = 14.087 studs 2 studs x 17 plates = 7.088 studs 8 studs x 3 plates = 8.089 studs 8 studs x 29 plates = 14.091 studs 14 studs x 4 plates = 14.091 studs 10 studs x 12 plates = 11.092 studs 10 studs x 17 plates = 12.093 studs 5 studs x 19 plates = 9.097 studs 13 studs x 4 plates = 13.098 studs

These are ranked with the most accurate fit first. Entries towards the bottom of the table are probably unusable:

6 studs x 9 plates = 6.997 studs 12 studs x 18 plates = 13.994 studs 2 studs x 27 plates = 10.984 studs 6 studs x 23 plates = 10.984 studs 3 studs x 29 plates = 11.982 studs 1 studs x 7 plates = 2.973 studs 7 studs x 14 plates = 8.964 studs 2 studs x 14 plates = 5.946 studs 4 studs x 11 plates = 5.946 studs 4 studs x 20 plates = 8.944 studs 8 studs x 10 plates = 8.944 studs 6 studs x 13 plates = 7.940 studs 5 studs x 8 plates = 5.936 studs 14 studs x 13 plates = 14.935 studs 7 studs x 21 plates = 10.934 studs 11 studs x 17 plates = 12.932 studs 5 studs x 12 plates = 6.931 studs 10 studs x 11 plates = 10.925 studs 12 studs x 12 plates = 12.924 studs 3 studs x 21 plates = 8.920 studs 1 studs x 12 plates = 4.903 studs 5 studs x 27 plates = 11.901 studs

Steve Baker <steve@sjbaker.org>