LEGO Building Techniques – Half Stud Offsets

Note: An updated version of this post has been published here.

When you are building with LEGO, you are always working with a grid of possible locations where you can place your bricks. For each layer of bricks you place, this grid is determined by the layer immediately below it. All the locations in this grid are separated by increments of a stud (which is the width of the basic LEGO unit – a 1 x 1 brick). For instance, if your first layer is a 32 x 32 baseplate, the bricks in your second layer have to be placed such that their studs line up vertically with one or more of the 32 x 32 studs in the baseplate. 

Say you are stacking bricks to build a tower that is supposed to taper as it rises. The smallest amount you can normally set back a layer of bricks relative to the layer below it is a single stud. Depending on the scale you are using for the tower, a full stud setback at each step may not give you as smooth of a taper as you would like. What if there was a way to set your bricks back by just half a stud instead of a full stud ? Fortunately there is a way, and that is using jumper plates. These are plates that have studs located halfway between where the studs would normally be, on a regular plate. They allow bricks to be offset by half a stud in one or both dimensions.

Tapering in one and two dimensions with full stud and half stud offsets

While the 1 x 2 and 2 x 2 jumper plates have been around for a long time, the 1 x 3 and 2 x 4 jumper plates are more recent additions to the LEGO catalog.

Jumper plates can also be used to push windows or wall sections back by half a stud to add more subtle detail. Here are examples from two of my skyscraper models. In the case of the Empire State Building, I used jumper plates to create recessed wall sections at the top of the building and also to taper the portion of the building that leads up to the spire.

I did something similar in my model of 70 Pine Street. Here, jumper plates were used to create recessed windows as well as for the taper at the top portion of the building that culminates in the spire.

Three of my skyscraper models (Transamerica Pyramid, John Hancock Center and Vista Tower) use half stud offsets extensively to create tapers that stretch the entire length of each building. One complication with half stud offsets is that the edges of your bricks are no longer in a straight line and so, if the portion of your wall that uses half stud offsets needs to meet a regular wall, you are left with ugly gaps. I had this issue on my model of the Transamerica Pyramid where the “wings” of the building intersect the main tower. I ended up using tiles attached to the wings to plug these gaps as best as I could.

In the case of the John Hancock Center, I had to deal with a different kind of issue. Based on the dimensions of the real building, I realized that the wide and the narrow side of the model needed to be tapered by different amounts in terms of studs. So I couldn’t simply use the 2 x 2 jumper plates like I did on the Transamerica Pyramid. I had to use a mix of 1 x 2 jumper plates (oriented lengthwise or widthwise) along with 2 x 2 jumper plates to taper the model by one stud (half stud on each side) every 6 floors (on the long side) and every 8 floors (on the short side).

LEGO Building Techniques – SNOT

Did you know that my skyscraper builds have taken a lot of hard work ? In fact, you have no idea all the blood, sweat, tears and SNOT that went into them ! Sorry I couldn’t resist, but SNOT here refers not to a bodily fluid but a LEGO building technique (it stands for “Studs Not On Top”). Who came up with these LEGO acronyms anyway ? From AFOLs to MOCs to SNOT, the acronyms used by the LEGO community are anything but elegant, but I guess we are stuck with them for now.

Anyway, SNOT refers to a technique where, in addition to stacking LEGO bricks, plates and tiles the normal way (one on top of the other) we are also turning them on their sides and attaching them to the faces of other bricks. As the LEGO system has evolved over the years, more and more elements have been added to the LEGO catalog that are designed to facilitate this – especially bricks that have studs not just on the top but on their sides as well. Here are examples of some SNOT elements that I have found to be very useful.

SNOT is not as straight-forward as it sounds and the reason is the geometry of LEGO bricks. A basic 1 x 1 brick has a footprint of 0.8 cm x 0.8 cm and a height of 0.96 cm. In other words although the footprint of a brick is a perfect square, it is taller than it is wide. If we use a plate (0.32 cm high) as a unit of measurement, a brick is exactly 3 plates high but only 0.8 / 0.32 = 2.5 plates wide. A stack of two bricks would be 6 plates high but a 1 x 2 brick turned on its side would only be 5 plates high. To match the height of the 1 x 2 brick turned on its side, we would instead need a stack of 1 brick (3 plates) and 2 plates. This 2 studs = 5 plates equation is something that always comes into play with SNOT.

I cannot possibly cover all the different applications for SNOT here, but I can give some examples from my own skyscraper builds where it would not have been easy for me to achieve a certain detail or shape without using SNOT.

My first example is some simple SNOT I used for the base of the Empire State Building. Here I wanted the windows to be slightly recessed compared to the walls and an easy way to achieve that is by attaching tiles to the wall sections between the windows. With the 1/230 scale I was using, I needed each floor to be 5 plates high anyway and this was perfect for SNOT. I had layers with bricks sandwiched between layers with plates. I used the 1 x 1 modified bricks with two adjacent studs in the corners and 1 x 1 modified bricks with single studs everywhere else and attached 1 x 6 tiles to the wall sections between the windows to achieve the recessed windows effect.

It was a little trickier to create the same effect on the base of my model of the Hearst Tower. Here the scale is bigger (1/156) and calls for 7 plates per floor. To be able to attach 1 x 8 tiles to the faces of the wall I needed to somehow get the studs on the faces of the walls to be 5 plates apart even if each floor was 7 plates high. I ended up having to mix bricks and plates within the same layer (so to speak) to achieve this.

Next we look at a more complex example of SNOT. I couldn’t think of an easy way to recreate the curves of the crown of the Chrysler Building. Simply stacking bricks or plates would have created a very blocky structure and I knew I had to find a way to incorporate some curved slopes pieces which have smooth curved surfaces. After quite a bit of experimentation using LEGO graph paper, I figured out a way to do each of the 6 arch panels (of varying sizes) using a combination of regular bricks and plates as well as their SNOT counterparts with studs on their sides, in addition to tiles, brackets, etc. I also found a way to join these panels together to create a sturdy structure for the crown that would hold together without any glue.

My last example is another tricky roof – this time it’s the roof of 40 Wall Street. Again, there was no easy way to build the green pyramidal roof of this building just by stacking bricks or plates. I figured I would need to build the green roof panels entirely out of plates and have them angled using hinges. Each roof panel was exactly 30 plates wide so that it could be attached to the base that was 12 studs wide. Also each panel was built in two halves (with studs facing opposite directions) that were joined together using SNOT.

Designing a LEGO skyscraper – part I

What exactly is involved in designing a LEGO model of a real skyscraper ? I wish I had a knack for doing it by eye – intuitively figuring out how wide (in terms of studs) and tall (in terms of brick heights) the model needs to be just by looking at pictures of the real building. I am sure some people can pull it off but this approach is clearly a hit-or-miss for many others (which is the only way I can explain all the models I have seen that are badly out of proportion compared to the real building).

Being an engineer, I tend to rely on a more rigorous approach based on math (very simple math as it turns out) instead of using just my eyes and intuition. The first step is picking the scale that works best for the model. The scale is just the relative size of your model compared to the actual building – expressed as a ratio. So a 1/100 scale simply means that your model of a 500 foot tall building would stand exactly 5 feet tall. Now, this 1/100 ratio applies to all the dimensions in the model – not just the height. And so if the actual building is 100 feet wide, your model would have to be 1 foot wide or it would not have the right proportions (it would either look too skinny or too squat compared to the real building).

There is obviously a trade-off associated with scale. The bigger the scale, the more accurately you can represent all the elements of the original building in your LEGO model. But too large of a scale can also result in a massive, unwieldy model with a prohibitively high piece count and cost. On the other hand, using too small of a scale can force you to compromise on accuracy (probably more than you would find acceptable). I try to find the sweet spot with my skyscraper models – a scale that is somewhere between the tiny scale used in the LEGO Architecture series and the huge scale used for the models you would find in a LEGO Miniland. In fact, the scale I pick is usually the smallest one that would allow me to accurately represent the floor count and the window count of the original building.

Let me use the Empire State Building as an example – to show how I arrived at the 1/230 scale I ended up using for my model of this building. The first step is getting the dimensions of the real building and here Google Earth proves to be very useful.

As you can see from the 3D view in Google Earth, the Empire State Building tapers as it rises and there are 7 distinct sections that make up the building. The largest section is the main tower (as I call it) which spans 42 stories (floors 30 through 71) and I am going to use that to determine the scale of my model. Not everyone is aware of this, but you can use Google Earth to make very precise measurements. I can zoom into a specific area in the 2D view and hit the ruler icon to make a measurement. I did this on my phone and measured the footprint of the main tower to be 184 x 134 feet.

Next I take a closer look at the window configuration in the main tower. On the longer side the main tower has windows arranged like this

-xx-xxx-xx-xx-xx-xx-xx-xxx-xx-

(where x represents a window) with the middle portion recessed. There are 2-wide and 3-wide banks of windows but one nice thing about this building is that all the individual windows have the same width which is also similar to the spacing between the different banks of windows. So if we were to represent each window using one stud, the longer side of the tower would be 30 studs wide. The shorter side has 7 banks of 2-wide windows

-xx-xx-xx-xx-xx-xx-xx-

and that adds up to a total of 22 studs.

Next we figure out what scale we would be using if we have 184 feet represented using 30 studs. Here are some of the key dimensions of a LEGO brick – it is 0.8 cm wide and 0.96 cm tall. Three plates are equal to a brick in height and so each plate is 0.32 cm tall.

If each stud is 0.8 cm wide, 30 studs would be 30 x 0.8 = 24 cm wide. We need to convert the width of the real building into metric units as well. 184 feet is roughly 5608 cm (1 foot = 30.48 cm). So our scale ends up being 24/5608 or roughly 1/230. We arrive at roughly the same number if we use the dimensions of the shorter side (134 feet) and the 22 studs we would be using to represent it in our model (22 studs = 17.6 cm, 134 feet = 4084 cm. The scale is 17.6/4084 = 1/230).

Once we have the scale, it is easy to know how tall our model will be – just divide the total height of the Empire State Building (1454 feet) by 230 and you get 76 inches (6 feet, 4 inches). Next, we need to figure out how tall each floor of the building will be in terms of brick heights (actually I prefer to use the smaller unit of plate heights). In most older skyscrapers, each floor is typically 12 feet tall. This is also the number you get when you divide the total height of the building (1250 feet which is the roof height not including the spire) by the number of floors (102). So the main tower should be 42 x 12 = 504 feet tall. It turns out this estimate is close enough to the actual measurement of 502 feet from the drawing at this link.

So how many plates does 12 feet translate to ? 12 feet are equivalent to 12 x 30.48 = 366 cm which in our model should translate to 366 / 230 = 1.59 cm. This is equivalent to 1.59 / 0.32 = 5 plates. It is important to keep this in mind when we design the model. We may be tempted to just use 2 brick heights (6 plate heights) per floor to make our lives easier but that would just make the final model 15 inches taller than it needs to be (the proportions just would not look right).

Now, not everyone has the wherewithal to build a model that is over 6 feet tall using (as it turns out) 20 K pieces. So what do you do if you want to build something smaller ? Then, it’s basically a matter of balancing your target size/cost for the model with the compromises you are able to live with in terms of accuracy. The first model I built when I got into this hobby was actually a smaller version of the Empire State Building. It used a smaller scale (1/360). Here I used 19 studs for the wider side of the main tower instead of 30 and one of the compromises I had to make was to use a single stud to represent each of the 2-wide and 3-wide banks of windows. Clearly I was not happy with what I had to give up in terms of accuracy with this model and that is what led me to build the bigger, more accurate version that I now have.

Empire State Building – a comparison of the different LEGO versions

My daughter who helped me build my custom model of the Empire State Building also happened to build the most recent official version (set 21046). She built it all by herself which is quite an accomplishment for an 8 year old (especially given all the complex SNOT techniques that this set uses).

LEGO had previously released a much smaller stand-alone version (set 21002) which was just 7-8 inches tall and devoid of any details (I personally find it to be one of the most disappointing sets in the Architecture series). There was another version of the Empire State Building in the New York skyline set (21028) that LEGO released. This used the 1×2 grille tiles to add a little more detail but the scale was about the same as what was used on the original set. I am happy to report that the new set (21046) leaves the previous two versions in the dust. It is amazing how accurate the designers of this set managed to make it at such a (relatively) small scale. The very clever SNOT techniques used to clad the facade of the model with 1×2 grille tiles make the building process very interesting (albeit a bit tedious).

After watching my daughter build the 21046 set, I was tempted to do the same digitally. I took the opportunity to build all 3 official versions in stud.io so I could compare them to each other and also to my much bigger custom version.

Update :

In April 2021, I challenged myself to build a version of the Empire State Building that is somewhere between the official (21046) set and my 6-foot tall version.

The outer shell of this model was entirely built using SNOT and the scale worked out to be 2x that of the official set (and half that of my big custom version – which would make it around 3 feet tall if built using real pieces). The piece count of just the outer shell was starting to push 10000 pieces and I hadn’t even worked on the inner core. I ended up abandoning this effort but not before I did some renders comparing the models at 3 different scales.

LEGO model vs. the real building – a comparison

A true test of the accuracy of a LEGO model is putting it up against a picture of the real building to see how well it holds up in comparison. I have tried this with a couple of my models (using digital renders that match the real pictures as closely as possible in terms of the angle of the shot and lighting). Here are the results

Empire State Building – real vs. LEGO model
Transamerica Pyramid – real vs. LEGO model