I’ve always been fascinated with building angles with rectangular plates and bricks. For a while, I thought that Pythagorean triples are the only way to go. Until I built this set, the original winter village toy shop. It’s able to create all of the Christmas tree’s angles with only normal plate with a simple and yet intriguing technique. I call it the diagonal building technique.

This technique uses the fact that the distances between two diagonal studs are the same, no matter where the pair of studs are. For example in the Christmas tree above, the distance between two diagonal studs is always:

a=1/sin(atan(1/3))=3.16228 studs

The exact distance is not that important, since you cannot recreate this distance with rectangular bricks in any other way, except with two diagonal studs. And when you overlay two different sets of diagonals you get an angle other than 90°.

This technique works on any two 2×4 diagonal studs. It doesn’t have to be two 2×4 plates. One can be 2×4 and the other can be bigger, or both can be bigger.

So it gives you an easy way to create an angle between two plates. To get more support and connection points between two large plates, you can add a stud to every 2×4 diagonals, such as below.

This works with any size of diagonal pairs, 2×3, 2×5, 2×6 and so on. The possibility is unlimited.

*Related*

Cool breakdown! Have you seen Niels’ old article about this? It might be of interest when you decide to explore this further: http://www.l3go.bugge.com/articles/technique/Hypotech1.shtml

Thanks. This is very interesting. I’ve not seen this article. It uses two hinge plates to create various angles. I’ve only seen triangles done with 3 hinges.

I have two follow on posts coming. Part of it will talk about how I use hinge plates.

There is a similar technique used in some of the larger LEGO airplane models (like Sopwith Camel) to taper the fuselage towards the tail. If you put a 1×4 hinge (either plate or brick) at each end of some bricks, with the hinge part on opposing sides, you can shift one side two studs to the side and the two ends will still fit the same grid of studs, with the middle part on a diagonal.

Yes, I forgot about that set. My next post is about using hinge plates. I’ll add Sopwith Camel as an example. Thanks, Bill.