As that great sage Ralph Wiggum says, "I'm learnding!"
About this creation
In the interest of promoting knowledge and accelerating the learning curve among those who haven't yet discovered the following ratios, I present to you a few tips and tricks that I've found useful in my own building.

Everyone knows that a standard Lego brick is three standard Lego plates high. This is quickly discovered in our earliest days of basic studs-up building.
But there comes a time when you need to graduate to more advanced SNOT (Studs Not On Top) techniques to achieve a certain look or texture impossible with simple studs-up brick and plate stacking.

When you integrate an element with the studs facing at right angles to adjacent or surrounding construction, you need to know the ratio between plate height and stud width. This ratio, which I utilize over and over again in my building, boils down to: five plates height equals two studs width.
This is important enough to bear repeating: 5 plates high = 2 studs wide. Note that the studs themselves are not counted in the height of a plate -- thus, more accurately but longer to write, four plates and one tile equals two studs. For purposes of this tutorial, when I refer to plate heights, I am not counting the topmost studs. When utilizing this technique, you will need to swap out the top plate for a tile, or somehow account for the studs (see below).

Here we see that two bricks height (6 plates) minus the bottom tile (1 plate) gives us a quick and easy 5 plates high / 2 studs wide gap to slip our SNOTed plate stack into.

Knowing this ratio (and as long as you can count by twos and fives), you can now completely fill any space whose length and width can be measured in an even number of studs. 4 studs = 10 plates. 6 studs = 15 plates. And so on.

The magic doesn't stop there. A floor made of these SNOTed plate stacks will, without effort, match up right at the 3 plate level when laid directly on a bed of studs beneath. This works because if 2 studs = 5 plates, then 1 stud = 2.5 plates... and the height of a stud itself = half a plate.

Because everything works out so nicely, you can then easily build out onto this floor and lock it into place if you haven't already -- otherwise nothing holds it in but gravity (or friction if it's vertically oriented in a wall), and if you tilt the base far enough, it will fall out.

To lock it in place without this, you'll need technic bricks (or headlight bricks, see below). The studs on a standard plate will fit into either two 1x1 technic bricks or the 1x2 with two holes. Or the one stud on a jumper plate will fit into a regular technic brick with the hole in the middle. To fasten the underside plate, use the technic brick / half pin combo or some kind of brick with studs on the side.
This fastening can also be done with brackets and headlight bricks, which have ratios of their own which must be taken into account.

Brackets and headlight bricks make use of half-plate offsets. Let's talk about the headlight brick (hereafter referred to as an HB) first.

What is a stud's width measured in plate height? If you said 2.5, good, you've been paying attention. The HB recess is half a plate deep, making the top of a HB, measured front to back, 2 plates wide. The little lip at the bottom created by the recess is also half a plate high.

Here we see that the extra half plate afforded by the recess on the HB allows us to bridge a 1 stud gap.

Or, since we're now aligned perfectly on a stud edge, begin counting off further 5 plate/2 stud increments. Through use of the mighty HB, we have broken the surly bonds of even-numbered stud width SNOT surfaces.

With their inherent height of 3 plates and top width of 2 plates, four HBs fastened perpendicularly will make our magical 5 plate/2 stud square.

The studs and holes line up neatly to plug into other such squares, making all sorts of interesting patterns possible.

Of course, when using this technique in a floor or wall, the outside studs must be taken into account.

Whereas the SNOTed element of the HB is recessed half a plate, the overhang on the bracket sticks out half a plate.

Add two plates and the overhang equals one stud wide.

In case you're a bit slow on the uptake, here is a bracket alongside two HBs with a plate to make up the difference in offsets.

A baseplate is the same height as the overhanging SNOTed part of a bracket, half a standard plate. Since the height of a stud itself is half a plate, we can lay a baseplate on a bed of studs, and the level of the baseplate will be one standard plate high.
This is by no means meant to be a comprehensive list, just a few of the basic tricks to get you started. Hope you found it helpful.
Addendum/mea culpa:
As for plugging studs into Technic brick holes, it evidently is "illegal," as illustrated here by Ryan Wood. Close enough to fudge it in most cases, but not exact.
Comments
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November 14, 2012 |
I gotta bookmark this! Thanks for the tip! |
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October 6, 2012 |
I remember seeing this way back when, I can't tell you how much I tried to look for it. THANK GOD IT'S HERE :D |
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October 6, 2012 |
Congrats on MOTD! This was one of the mocs I added to my Favorites very early on in my stay here! :) |
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October 6, 2012 |
Interesting, I'll have to keep this in mind when building! =D |
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October 6, 2012 |
I believe thanks are in order. About two years ago, when I was somewhat new to the online LEGO community, I looked at this. It helped make me become the builder I am today, and I learned a lot of useful techniques. I salute you, master of the Skunk Works, and thank you once more. |
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October 6, 2012 |
thanks for this, really useful! Ive been meaning to get back into system moccing. |
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October 6, 2012 |
Thanks for the tips! ;) Congratulations on MOTD! |
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October 6, 2012 |
Well deserving of MOTD. |
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October 6, 2012 |
Great stuff, and good to remember! |
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October 6, 2012 |
Fancy, stuff. I need to remember these tips. |
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October 6, 2012 |
Great job! :) and great tips for biginners! maybe they could use this one, too: try to push a plate between two studs, it will fit, I used this more than one time :) |
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October 6, 2012 |
I love the way how you've managed to include so many ratios into the small build in the first photo. The rest of the pictures illustrate techniques simply & clearly. Great work and a useful resource. |
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October 6, 2012 |
LOL! I already saw this creation yesterday. This 'lesson' will be helpful! |
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October 6, 2012 |
Very helpful! And MOTD! |
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October 6, 2012 |
excellent! very helpful! 'grats on MOTD! |
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April 19, 2012 |
It is good to see all of these listed here in one place. I would add one more, though, that I have found very useful. When you want to attach a plate facing outward using a brick with a perpendicular stud if you separate each brick with two standard platform bricks then they will fit into every other connector on the back of the plate. I use this technique a lot if anyone wants to see an example. |
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March 23, 2012 |
"I'm learning!" XD |
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February 22, 2012 |
That's a great tutorial! It's good to have all these photos to look at them anytime. Thanks for that, great job! :-)) |
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January 6, 2012 |
I never seen this one !!!! so cool to share !!! It will be very helpful !!! |
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January 5, 2012 |
Brilliant! I've seen and used quite a few of those before, but a couple of them are new to me. Thanks for posting this! |
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November 18, 2011 |
Nice! Although, the stud-into-technic-hole isn't actually illegal, it's a technique used by LEGO. |
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November 17, 2011 |
many thanks for the lesson, teacher! =) |
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June 15, 2011 |
I luved it! Also, I'm new to all this and found you thru you being a favorite of another MOCer who I like. Then recalled having seen some of your MOC's before....I wonder about that mind of yours...that's a complement from a fellow Pacific Northwesterner! |
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Joel S. April 18, 2011 |
wow. this is very interesting. i never thought there could be so many combinations like this. the last part with the baseplate will REALLY come in handy! 10 out of 5, my friend. 10 out of 5. |
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Rolling bricks April 18, 2011 |
Interesting! |
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April 18, 2011 |
saving and faving and commenting |
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April 18, 2011 |
Genius!! Thanks for the amazing tips. |
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April 18, 2011 |
Of course you would want viewers to use these techniques! So I just might! Nice job! |
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April 18, 2011 |
Very useful and interesting information! Thank you! |
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April 18, 2011 |
Thanks for sharing. I have used some of these techniques but not all. Also really like the colours you have used. Congrats on motd |
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April 18, 2011 |
the pics with 4-8 headlight bricks together make little nazi signs. subliminal LEGO? congrats on MOTD. |
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April 18, 2011 |
Math and legos, sweet! |
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ahh... usless numbers and facts... Love it! xD |
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April 18, 2011 |
This is very useful information! |
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April 18, 2011 |
Ahh, I love math! This is my kind of thing.
Ooo! Here's some different techniques I haven't noticed before. Thanks! |
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April 18, 2011 |
I hate math, so when I saw the title to this MOC, my mood turned sour. However, that all changed when I actually viewed your pics and description and realized your creation was about LEGO building. I gotta say, this MOC has been extremely helpful! I'm even starting to like ratios...well, maybe not :) Congrats on MOTD! |
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April 18, 2011 |
This is very very very helpful!! |
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April 18, 2011 |
Why can't Math Ratios be this easy? -Lee |
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April 18, 2011 |
This is a quite interesting lecture.
I knew some of the basic things already (as you said: discovered in our early days), but there where a lot of possibilities I did not know so far. |
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April 18, 2011 |
Very Informative! :-) |
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April 18, 2011 |
Thats good information to know, i will need to remember them. and congrats on MOTD!-Tchexmix |
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April 18, 2011 |
awesome work! This is really useful! and congrats on MOTD! |
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March 10, 2011 |
Wow! ive never even remotely considered some of these techniques! thanks for the knoledge, I plan to use it. |
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March 6, 2011 |
Nice basic techniques but there's a mistake in it. A stud's height is equal to 1/4h, not 1/6h. |
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November 18, 2010 |
This has probably been the single most helpful MOC I have ever seen, it has improved my creations by far, thanks. |
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November 13, 2010 |
This is the greatest thing ever. I always thought that 2 studs width=4 plates high! Thank you! |
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August 23, 2010 |
Great tutorial. Thanks.
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May 22, 2010 |
Technically the "HB"s are called Earlings
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some of that stuff I was finally getting my head round through trail and error. One thing though, a couple of the examples use the technic bricks with studs pressed into them. is that an official construction technique as it isn't possible in LDD. I only ask as I wondered if it stressed bricks when using it in real life. EDIT: someone asked this, not me.
Well, in LDD, you first have to put two 1X1 circular flats on the piece you want to stick in the Technic brick. BTW, that MOC is Smart! I would never have figured some of that out, considering i'm still just 9. |
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April 23, 2010 |
Really useful 101. Very well explained. Now let`s see 28 studs high, 80 studs wide, plates vertical 90 degrees, that means..... |
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I made it |
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April 1, 2010 |
Quoting andros tempest
One thing though, a couple of the examples use the technic bricks with studs pressed into them. is that an official construction technique as it isn't possible in LDD. I only ask as I wondered if it stressed bricks when using it in real life.
Well, I've found that plugging a stud into a Technic hole can sometimes be a tighter fit than plugging it into the bottom of another brick or plate. Might be a tiny bit of stress involved, but I personally would never have thought of it as an "illegal" technique. Maybe an oversight on the part of the LDD program writers? |
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March 31, 2010 |
some of that stuff I was finally getting my head round through trail and error. One thing though, a couple of the examples use the technic bricks with studs pressed into them. is that an official construction technique as it isn't possible in LDD. I only ask as I wondered if it stressed bricks when using it in real life. |
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March 30, 2010 |
Great page, the 4 interlocked 1x1 light pieces is something I have never thought or seen of before. Great presentation on this, I'm glad I finally checked it out... |
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March 26, 2010 |
Very colorful. I've used that thing with the brackets on my hangar dios for awhile now. Thanks for the ideas. |
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March 10, 2010 |
every bit as informative as the "Chronos Project" was funny. Your next batch of red tiles are in the mail... |
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Blade Bat February 26, 2010 |
No your giving away all my secrets. |
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February 26, 2010 |
can you imagine how much more effective our space program would be if NASA commissioned their mathematics from LEGO engineers? |
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February 26, 2010 |
Today is a good day Mr. Young - it is always a good day when I learn something new, and here you have taught me a couple of new techniques. Thank you. Lee. |
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February 26, 2010 |
thanks for posting! this stuff will be so helpful. alot of these i have seen before and sometimes used, but there were some really good ones that are new to me. thanks! |
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February 24, 2010 |
True, these techniques can a help a lot when you're designing something. |
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February 23, 2010 |
thanks |
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Elk . February 22, 2010 |
Wow. That is very thought provoking. I will use that sometime. |
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February 21, 2010 |
SUM DAEY YOO CAN HAS MATHS T00
Thanks for the ratios. You should make another one of these but for hinges (example- these pegs on the rod part of a fire piece can fit on the visor holes of a clone trooper helmet, allowing you to make a flaming helmet.)
I do alot of stuff like this, I call it "Abstract Lego" |
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Okay, I never realized the thickness of the baseplates. I'm gonna have to try that sometime. |
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February 21, 2010 |
I am going to use it well, thanks |
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February 21, 2010 |
Excellent, I love instructional MOCs and you did a great job on this one Shannon. Ratios are a tricky thing, I had mostly figured these all out, but I didn't realize that baseplates are half studs and can be stacked as such in your last picture. Learn something new every day I guess. Thanks for sharing |
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February 20, 2010 |
cool, I just love how Legos fit together no matter what the problem. |
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I read this and was like... Huh? |
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February 20, 2010 |
holycrap! i need those ratios thank you :D |
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February 20, 2010 |
Didn't know some of those ratios myself. Invaluable for anyone new to the SNOT technique. |
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Dave Sterling February 19, 2010 |
An excellent visual representation of the multitude of SNOT techniques out there. Great work Shannon and thanks for posting this. I hadn't seen the 'four headlight bricks form a square' technique before. Nice work! |
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February 19, 2010 |
Love it. Great stuff, that will hilp me with my floors. But ive already been to Math today... and I hate math so much. |
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February 19, 2010 |
Thanks. I'm actually going to favorite this. |
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February 19, 2010 |
Most impressive. To be honest, I had never seen half of the ideas you presented. Very well done, specifically that last item. |
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February 18, 2010 |
a brilliantly constructed tutorial to people who have yet to realise all techniques and at the same time a good reference and reminder for those who already know some if not all of them. I use these here and there in the occasional moc i never publish because of current internet upload prices, but it is good to have things like this to remind me how i did it and to proove to myself i am not just bending bricks but they actually fit :P |
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February 18, 2010 |
Quoting MegaKid T1
I already did that.
Congratulations. Good thing for you this isn't a race to the south pole, because I figured out the headlight brick square trick around 1980, long before you were ever thought of. Nowhere on this page did I claim to invent any of these techniques, or be the first to discover and employ them. It's just meant to be a handy reference guide for those who haven't yet discovered them. If you've already got it all figured out and this page is of no use to you, then more power to you, genius.
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Neat. But the one with the 4 two-stud-two-indent connection part, I already did that. Almost with the same color! Sorry, but 3 heads. |
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February 18, 2010 |
Great stuff. This is my new reference material. |
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February 18, 2010 |
Well done sir, seen a lot of this before but presented in a far more stuffy, math-heavy form on some word document. This was far easier to follow and nicely done. |
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February 18, 2010 |
Quoting Dax Olesa
I may point out, however, that the third-to-last technique displayed here is not exact.
A valid point -- in fact I don't know that I would call any of the above ratios "exact." Lego pieces are not perfect, and sometimes the tolerances will be microscopically off. When you're working in small increments it usually isn't a problem, but over longer distances the slight misalignments can add up and become noticeable. You check and re-check the math, you're sure that it's right... but the pieces just refuse to abide by it.
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Spaztastic the Diabolical February 17, 2010 |
I've been thinking about these for a while, but every time I started experimenting, I lost focus and started configuring weapons. Also, there are lotsa... rainbows. Just to let you know. |
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A member of Starfox . February 17, 2010 |
Just a few pieces put together in different ways got you THIS many views and "I like it's". Just... WOW. I am horriable at SNOT. But a rainbow of colors in each picture gives it a more "fun" look to it. Those headlight pieces are hard to work with. And I NEVER knew about the base plate trick. Mine are bent. But they are now hilly. I may go try it soon. 5,000,000/5 for Mr. Shannon. |
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February 17, 2010 |
There are some techniques in here that I have been experimenting with, albeit badly, finding this little self help gem will greatly assist me in certain builds. Thank you very much. |
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February 17, 2010 |
nice though i will probabily forget this it will still come in handy wen SNOTing |
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February 16, 2010 |
This is awesome, thanks for posting it. |
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February 15, 2010 |
You, my friend, are Epic. |
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February 14, 2010 |
Sweet |
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February 14, 2010 |
Nice! This is just what a lot of people need. |
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February 14, 2010 |
Thanks, very helpfull indeed! But every build is different so I just keep trying for the best solution ;-) |
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February 14, 2010 |
Very nice collection of findings here. I've found out most of these over time, but I did learn some of the more advanced techniques right here on this page. I may point out, however, that the third-to-last technique displayed here is not exact. While working on my "Green Hell" diorama, I used that method to transfer from the SNOT base to the the studded sides of the track. After completion, I noticed hairline cracks between the green plates held on top. These small gaps added up to make, say a 8x1 tile, a little stretched over the pieces: not quite a perfect fit. This observation is very subtle, however, and it will not make a difference in most applications of the technique. A helpful strategy, nevertheless, and congratulations on this nice collection of building methods! |
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February 14, 2010 |
Wow, this is very good, and very helpful to people who never thought of this before. |
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February 14, 2010 |
I lernded. |
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February 14, 2010 |
The amount of rainbows in this MOC makes me worry.....
Nothing here I hadn't learned by accident, but I'm sure a load of MOCpages less observant builders will hopefully capitalize of you're kind teachings. |
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Noddles . February 13, 2010 |
I will never understand why this can't be a proper subject. Just look at the smartness in it! |
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February 13, 2010 |
Wow! Alot of this stuff I never knew (or at least never paid attention to) until now! Great job, and thanks for the lesson =) |
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February 13, 2010 |
Very helpful! Some of those I did not know and should definately be of use! |
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February 13, 2010 |
Quoting SoftaRae .
I don't get on the last one, though, why you mention the overhanging SNOTed part of a bracket in the caption.
Yeah, I phrased that badly. I just meant to reinforce the fact that a baseplate (like the side of a bracket) is half a plate high.
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February 13, 2010 |
THANK YOU! I previously made a mathematical table for LEGO ratios, but this is much more visual and contains more information than anything I could've written on paper. |
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February 13, 2010 |
Wow, very interesting! I hadn't realized several things in there... |
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February 13, 2010 |
Dude, thanks for the review! However, my mind went bezerk thinking of the math. ;) I also love the color matchups. |
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February 13, 2010 |
very educational if thats what it is supposed to be. |
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February 13, 2010 |
This is terrific, Shannon! Thank you so much for taking the time to do this ... and so well, too! I don't get on the last one, though, why you mention the overhanging SNOTed part of a bracket in the caption. There's no bracket in the picture, right? Is that just so we know you can use a bracket in the same way as the baseplate shown? Thanks again! |
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February 13, 2010 |
Excellent! -And as you say; The fun dosent even stop here! ;-) |
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February 13, 2010 |
I've stumbled across a little of this by accident, having it explained, demonstrated, and presented with possible ideas on how these techniques might be used is very valuable indeed. My hat is off to you sir, and I will certainly keep this post in mind as I start new projects. |
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February 13, 2010 |
In all seriousness, there is a lot here that I never bothered to explore myself. Thank you sir. |
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February 13, 2010 |
Very cool, I have to admit that I didn't know some of these. And you even said it better than my math teacher could. |
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February 13, 2010 |
very original,I'm sure it will be very useful. |
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February 13, 2010 |
Thank you very much. This Moc is going to come in very handy over the next month. My building is going to improve tremendously because of this information. You deserve a lot higher than a 5, but that's all I can give it. |
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February 13, 2010 |
Extremely useful, ta very much! |
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February 13, 2010 |
Pretty nice presentation, Shannon, though nothing I don't already know (not to brag). Though most of these techniques are pretty simple, I've always had trouble with the infuriating headlight bricks when it involves further complicated techniques.
Good day |
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February 13, 2010 |
Nice. I can use this tips when making some creation. Cool. |
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February 13, 2010 |
Wow thanks these are some techniques i could fide really useful, thanks alot :D |
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February 13, 2010 |
Like Moodswim and others, these are things I've only discovered through years of trial and error and there are a few things I hadn't known until now. Very educational and well presented. And hey, it got you a compliment from the man himself. Now, like Chris, I have some brain matter to wipe off my keyboard...~H |
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February 13, 2010 |
Sweet! That last one is awesome. I never knew that. some of this stuff will come in useful in my future building. :D |
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February 13, 2010 |
Very handy this is. Thanks for doing the thinking for me =D |
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February 13, 2010 |
So helpful! Thank you so much! |
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February 12, 2010 |
Dude, this is amazing. I knew some of these techniques (hardly use them though), but some of these just blew my mind! I always knew lego was good at keeping things compatible, but this has taken it to the next level! Well done. :) |
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February 12, 2010 |
Thanks! Now if I need to find something about SNOT I can refer back to here! |
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February 12, 2010 |
Thanks. I got many new ideas now but i don't have enough bricks of that sort to make these ideas true :( |
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February 12, 2010 |
The Great Shannon (young) has spoken... Much appreciation for sharing your boundless knowledge.... |
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Wow, I don't know what it is, but you're full of it! :D |
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I made it |
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February 12, 2010 |
Quoting Emperor Ludgonious
You should throw a link up to this in the MOCpages Advice Group.
I just couldn't handle the noise level in that group -- too much meaningless chatter, precious little "advice" being sought or given -- so I quickly left. But if you or anyone else wants to link to this, I won't turn down the free publicity.
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February 12, 2010 |
Thanks for posing this tutorial. I know alot of this stuff already but a few of them I didn't know. I will have to try some of them. ~ J |
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February 12, 2010 |
I'm bookmarking this! |
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February 12, 2010 |
Excellent descriptions of the basic ratios and and some of the more advanced building techniques associated with them. You should throw a link up to this in the MOCpages Advice Group. |
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February 12, 2010 |
You do realize of course that my head just exploded from having to follow math right? ~ Chris. |
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February 12, 2010 |
I love your use of colors here to so clearly illustrate what can otherwise be a real mathy-pain. Bravo, and here's hoping many can learn from this great tutorial!! |
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February 12, 2010 |
I thought I knew everything here until I saw the last one.... I've always wondered about that..... |
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February 12, 2010 |
Great hints, and great presentation. |
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February 12, 2010 |
Nothing I didn't already know here, but well presented. I can't wait for you to get into some of the more difficult ratios (especially technic). |
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February 12, 2010 |
Thanks for this! I'm obsessed with making my builds studless. Most of these techniques I've learned from trial and error, but some of these I didn't and they will come in handy in the future. Not sure if you knew, but some of the newer Headlight bricks don't have the half-stud indent, making it even easier to use these pieces in SNOT or studless creations:) |
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February 12, 2010 |
I've just got to say thank you for this, the SNOT floors have been a mystery to me for far too long, and I've been forced to use standard tiling. You sir, have just earned your page a spot on my bookmarks. |
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February 12, 2010 |
Ingenious. I love the use of all the different colors for emphasis. -Sam |
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February 12, 2010 |
We are not worthy! XD |
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February 12, 2010 |
Quoting Thomas N
Shannon Young being helpful!?
If it's any reassurance, I'll try to make my next post cause mass anger and frustration.
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February 12, 2010 |
My gosh... Shannon Young being helpful!? What on earth has happened to the world? ~T |
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February 12, 2010 |
At first I thought this was a joke, but then I read on. Nicely said. -Dylan |
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February 12, 2010 |
This is one of THE most useful MOCs I've ever seen! I worship you. |
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Very cool, I like all the ideas of how to design different shapes. 5/5 Great demonstration! |
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February 12, 2010 |
interesting! |
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More from Shannon More across MOCpages
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