Answers.Body: <p>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 <a href="http://www.flickr.com/photos/62bricks/10120896015/in/photostream/" rel="noreferrer">this construction</a>:</p>
  
  <p><img src="https://i.sstatic.net/RevVz.jpg" alt="enter image description here"></p>
  
  <p>Likewise, the 8x8 corner plate has a diagonal edge that is very close to <a href="http://www.flickr.com/photos/62bricks/9918686074/in/photostream/" rel="noreferrer">10 studs long</a>:</p>
  
  <p><img src="https://i.sstatic.net/ldvJD.jpg" alt="enter image description here"></p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-03-15T01:15:18.520Z
Answers.LastActivityDate: 2014-03-15T01:15:18.520Z
Answers.UserDisplayName: 62Bricks
Answers.Body: <p>This is in old question but I think many people find this helpful.
  I accidentally found this Lego technique where you put a 4x4 round plate between four 1x1 round plates. You can see in the picture how to do it exactly.
  I think it is an &quot;illegal&quot; Lego technique. If you look closely you can notice that the distance between each 1x1 plate is a tiny bit more than four studs. And the cutouts on the side of the 4x4 round plate are designed for the normal four studs apart in my opinion.</p>
  <p>The turntable is just there so it doesn't come apart, but the 4x4 plate is fully locked by the four 1x1 plates themselves. It may look like it doesn't work but just try it out.
  <a href="https://i.sstatic.net/oT7ab.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oT7ab.png" alt="enter image description here" /></a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-27T16:57:46.343Z
Answers.LastActivityDate: 2022-01-28T12:17:47.610Z
Answers.LastEditDate: 2022-01-28T12:17:47.610Z
Answers.UserDisplayName: niklas10
Answers.Body: <p>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.  </p>
  
  <p>In most cases, tiles and plates in the right place will keep sufficient contact with the base plate to have a stable model.  <img src="https://i.sstatic.net/hvrPh.png" alt="hinges diagram"></p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-03-15T00:26:22.797Z
Answers.LastActivityDate: 2014-03-15T00:26:22.797Z
Answers.UserDisplayName: Windfire
Answers.Body: <p>Possibly I’m the same Woody that previously answered this question.  If so, I didn’t describe it well 5 years ago.</p>
  
  <p>This is a cut down version of the 7/7/10 triangle which is
  slightly better than the 5/5/7 triangle.</p>
  
  <p><img src="https://i.sstatic.net/iDVxb.jpg" alt="45 degree 3.5/3.5/5"></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-04-20T14:51:57.363Z
Answers.Text: Distance between two round plates is very close to allow 6 stud plate here, but unfortunately it is slightly shorter.
Answers.UserDisplayName: Alex
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-04-20T14:00:41.670Z
Answers.LastActivityDate: 2020-04-21T01:53:35.100Z
Answers.LastEditDate: 2020-04-21T01:53:35.100Z
Answers.UserDisplayName: Woody
Answers.Body: <p>If near enough is good enough you could build based on a 3:4:5 right angled triangle: i.e. put "dots" on the base plate 3 up and 4 across from each other which would then connect to the circles underneath a baseplate 5 holes apart.</p>
  
  <p>The angle would then be ~37 degrees or ~53 degrees between the two structures.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-01-12T05:34:02.210Z
Answers.LastActivityDate: 2017-01-12T05:34:02.210Z
Answers.UserDisplayName: Woody
Answers.Body: <p>Placing dots (1x1 round plates) on the bottom of one plate with 5 spaces in between will line up perfectly on a lower plate 4.5 down and 4.5 across (one dot fitting between studs on lower plate)</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-02-23T16:09:47.200Z
Answers.Text: Can you include some pictures to show what you're talking about here?
Answers.UserDisplayName: chicks
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-02-21T22:11:29.310Z
Answers.LastActivityDate: 2019-02-22T11:02:38.920Z
Answers.LastEditDate: 2019-02-22T11:02:38.920Z
Answers.UserDisplayName: stammy
Answers.Body: <p>45° angles are tricky because of the dimensions of 45-45-90 triangles:</p>
  
  <p><img src="https://i.sstatic.net/06TTJ.png" alt="45-45-90 triangle"></p>
  
  <p>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.</p>
  
  <p>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:</p>
  
  <p><img src="https://i.sstatic.net/lS01x.jpg" alt="continue offset example using transparent bricks"></p>
  
  <p>Edit: There is now a <a href="https://rebrickable.com/parts/15706/plate-special-4-stud-45%C3%82%C2%B0-angle-plate" rel="noreferrer">specialized 45° angle plate (15706)</a> that can be used for this purpose:</p>
  
  <p><a href="https://i.sstatic.net/t44L7.png" rel="noreferrer"><img src="https://i.sstatic.net/t44L7.png" alt="15706"></a></p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-03-14T23:24:32.033Z
Answers.LastActivityDate: 2017-01-12T14:55:27.257Z
Answers.LastEditDate: 2017-01-12T14:55:27.257Z
Answers.UserDisplayName: jncraton
Body: <p>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.</p>
  
  <p>What techniques are available to achieve this?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-03-14T20:02:29.530Z
Comments.Text: http://brickfanatics.co.uk/pythagorean-theorem-in-lego/
Comments.UserDisplayName: Courtny
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-03-14T21:39:44.050Z
Comments.Text: 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.
Comments.UserDisplayName: Ambo100
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-03-16T16:37:12.960Z
Comments.Text: 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.
Comments.UserDisplayName: Courtny
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-01-12T14:51:15.480Z
Comments.Text: All the techniques described above have one fault or another so have you tried to just get rid of the base altogether?
  I did that a couple of times when I needed to make angular walls and it works seamlessly provided you use some pieces from other brands because Lego doesn't make them.
Comments.UserDisplayName: Algern On
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-04-02T16:54:03.717Z
Comments.Text: https://toweringbrickcreations.com/2021/11/15/thinking-outside-the-grid-building-angled-walls-using-lego/#angled-wall-basics
Comments.UserDisplayName: Andrew Hodson
Tags: <building><angles>
Title: What techniques can be used for laying plates at 45° angle?
UserDisplayName: Courtny
ThreadText: # What techniques can be used for laying plates at 45° angle?
  
  (Asked by: username_0 on 2014-03-14)
  
  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?
  
  **Tags:** building, angles
  > **Comments:**
  > **username_0**: http://brickfanatics.co.uk/pythagorean-theorem-in-lego/  
  > **username_1**: 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.  
  > **username_0**: 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.  
  > **username_2**: All the techniques described above have one fault or another so have you tried to just get rid of the base altogether? I did that a couple of times when I needed to make angular walls and it works seamlessly provided you use some pieces from other brands because Lego doesn't make them.  
  > **username_3**: https://toweringbrickcreations.com/2021/11/15/thinking-outside-the-grid-building-angled-walls-using-lego/#angled-wall-basics  
  
  ---
  
  ## 7 answers
  
  ### Answer by username_11 on 2014-03-14. Score: 19 | Accepted answer
  
  45° angles are tricky because of the dimensions of 45-45-90 triangles:
  
  ![45-45-90 triangle](https://i.sstatic.net/06TTJ.png)
  
  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](https://i.sstatic.net/lS01x.jpg)
  
  Edit: There is now a [specialized 45° angle plate (15706)](https://rebrickable.com/parts/15706/plate-special-4-stud-45%C3%82%C2%B0-angle-plate) that can be used for this purpose:
  
  [![15706](https://i.sstatic.net/t44L7.png)](https://i.sstatic.net/t44L7.png)
  
  
  ---
  
  ### Answer by username_6 on 2014-03-15. Score: 18
  
  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](https://i.sstatic.net/hvrPh.png)
  
  
  ---
  
  ### Answer by username_4 on 2014-03-15. Score: 13
  
  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](http://www.flickr.com/photos/62bricks/10120896015/in/photostream/):
  
  ![enter image description here](https://i.sstatic.net/RevVz.jpg)
  
  Likewise, the 8x8 corner plate has a diagonal edge that is very close to [10 studs long](http://www.flickr.com/photos/62bricks/9918686074/in/photostream/):
  
  ![enter image description here](https://i.sstatic.net/ldvJD.jpg)
  
  
  ---
  
  ### Answer by username_5 on 2022-01-27. Score: 8
  
  This is in old question but I think many people find this helpful.
  I accidentally found this Lego technique where you put a 4x4 round plate between four 1x1 round plates. You can see in the picture how to do it exactly.
  I think it is an "illegal" Lego technique. If you look closely you can notice that the distance between each 1x1 plate is a tiny bit more than four studs. And the cutouts on the side of the 4x4 round plate are designed for the normal four studs apart in my opinion.
  
  The turntable is just there so it doesn't come apart, but the 4x4 plate is fully locked by the four 1x1 plates themselves. It may look like it doesn't work but just try it out.
  [![enter image description here](https://i.sstatic.net/oT7ab.png)](https://i.sstatic.net/oT7ab.png)
  
  
  ---
  
  ### Answer by username_7 on 2020-04-20. Score: 0
  
  Possibly I’m the same Woody that previously answered this question. If so, I didn’t describe it well 5 years ago.
  
  This is a cut down version of the 7/7/10 triangle which is
  slightly better than the 5/5/7 triangle.
  
  ![45 degree 3.5/3.5/5](https://i.sstatic.net/iDVxb.jpg)
  
  > **Comments:**
  > **username_8**: Distance between two round plates is very close to allow 6 stud plate here, but unfortunately it is slightly shorter.  
  
  ---
  
  ### Answer by username_7 on 2017-01-12. Score: 0
  
  If near enough is good enough you could build based on a 3:4:5 right angled triangle: i.e. put "dots" on the base plate 3 up and 4 across from each other which would then connect to the circles underneath a baseplate 5 holes apart.
  
  The angle would then be ~37 degrees or ~53 degrees between the two structures.
  
  
  ---
  
  ### Answer by username_9 on 2019-02-21. Score: -1
  
  Placing dots (1x1 round plates) on the bottom of one plate with 5 spaces in between will line up perfectly on a lower plate 4.5 down and 4.5 across (one dot fitting between studs on lower plate)
  
  > **Comments:**
  > **username_10**: Can you include some pictures to show what you're talking about here?  
  
  ---
  
  