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I've seen a number of techniques for laying individual elements at 45° angles, but I need a consistent method for laying down larger plates at 45 degrees while maintaining close contact with the base plate layer below it.

What techniques are available to achieve this?

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I've un-deleted this question because I believe others may benefit or wish to add to this question. If you have discovered a solution, feel free to add it as an answer to this question. –  Ambo100 Mar 14 at 21:39
    
I did come up with some solutions, but trying to come up with mathematically ways of scaling it to larger baseplates is where I am getting stuck. –  Courtny Cotten Mar 16 at 16:37

3 Answers 3

up vote 5 down vote accepted

45° angles are tricky because of the dimensions of 45-45-90 triangles:

45-45-90 triangle

The fact that the hypotenuse needs to be a multiple of radical two makes it difficult to build out of LEGO plates which are generally limited to integers or halves. The best you can do in a reasonably small amount of space is a 5 x 5 x 7.07 triangle, but that doesn't come close enough to work well.

I'm not aware of a way to do this using just plates, but if you are willing to use other bricks as well, there are some ways. For example, some older bricks and most transparent bricks don't include tubes within the bricks. This allows constructions that are not limited by whole numbers:

continue offset example using transparent bricks

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It appears that some LEGO pieces are designed with the proportions of 45-degree right triangles in mind. For example, the 3x3 plate with one corner removed has a diagonal edge that is very close to three studs long, as can be seen in this construction:

enter image description here

Likewise, the 8x8 corner plate has a diagonal edge that is very close to 10 studs long:

enter image description here

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Hinges can work, I have used this technique before, if you sandwich the hinges between two plates you get 45 degree 'bricks' that are quite solid.

In most cases, tiles and plates in the right place will keep sufficient contact with the base plate to have a stable model. hinges diagram

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