Don’t Underestimate That Jumper Plate – Half Stud Offsets in LEGO Models


What are half stud offsets and why do we need them ? Before we get into that, let’s start with the basics. A stud is not just the bump you see on the top of a LEGO piece that allows you to connect it to other LEGO pieces. It is also a unit of measurement representing the distance between two adjacent bumps (or knobs) on a LEGO piece (measured center to center). The basic building block of the LEGO system is a 1×1 brick which is exactly 1 stud wide and 1 stud deep (though it is a little taller than 1 stud). A 2×4 brick is 2 studs wide and 4 studs deep. All basic LEGO pieces (bricks and plates) have footprints that are multiples of 1 stud.

When you build with LEGO, you can only place each piece such that its studs (bumps) line up with the studs on the layer that is immediately below. If you start with a 32×32 baseplate, you are limited to a 32×32 grid of possible locations where you can place the pieces in your next layer and these locations are separated by increments of 1 stud (the measurement unit). Say you are building a wall where a section needs to be recessed. The smallest amount you can normally set the recessed section back is one stud. If you are looking to create a more subtle effect, would it be possible to set the recessed section back by just half a stud instead of a full stud ? Yes, and that is exactly what jumper plates allow you to do.

A 1×2 jumper plate (part 15573) has a single stud that is located exactly halfway between where the two studs on a regular 1×2 plate would be located. You can use it to set back (or offset) your wall section by half a stud as shown in the picture below.

Half stud offsets in one and two dimensions

While a 1×2 jumper plate allows you to create a half stud offset in one dimension (either front to back or sideways), you can do the same in two dimensions using a 2×2 jumper plate (part 87580). This jumper plate has a single stud exactly in the center of where the 4 studs on a regular 2×2 plate would be located.

LEGO has recently expanded their catalog to also include “double jumper” counterparts for their 1×2 and 2×2 jumper plates. They are the 1×3 jumper plate (part 34103) with 2 studs and the 2×4 jumper plate (part 65509) with 2 studs.

Creating recessed wall sections, windows, etc.

As we have seen, the 1×2 jumper plates are perfect for setting back sections of a wall or a window by half a stud to add more subtle detail. You may need another set of jumper plates above the window (a second half-stud offset to counter the first one) to get back to the normal alignment of the studs as you continue to build the wall above the window.

Here are examples of half stud offsets 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.

I did something similar in my model of 70 Pine Street. Here, jumper plates were used to create recessed windows.

Centering elements with odd vs. even number of studs

Another great application for jumper plates is centering an element with an odd number of studs relative to something with an even number of studs or vice versa.

The top portion of the Empire State Building has narrow windows (one stud wide based on the scale I was using) that needed to be centered relative to the windows below them (which were each 2 studs wide). I was able to use 1×2 jumper plates to center the smaller windows relative to the bigger windows below them.

In the digital model of the Blue Mosque that I built, I needed to have 3 smaller arched window openings inside a bigger arch. I used jumper plates to center the 3 smaller arches (with a total outside dimension of 7 studs) inside bigger arch with an opening that is 6 studs wide.

Smoother tapers using jumper plates

An obvious application for jumper plates is to help achieve smoother tapers than is possible with regular bricks and plates. Like many of the other skyscrapers built during the early 1930s, the Empire State Building and 70 Pine Street have top sections that taper as they lead up to their spires. I used 2×2 jumper plates for the tapers in my models of these buildings.

My models for other buildings like the Transamerica Pyramid and John Hancock Center required more extensive use of half stud offsets given that the entire buildings have tapered shapes.

The Transamerica Pyramid in San Francisco is a skyscraper with a square base that gradually tapers to a point at the top. Based on the scale I was using, I needed to taper the model from 28 studs to 7 studs over 42 floors. With regular bricks and plates, the smallest amount I would have been able to taper the model is 2 studs (one stud on each side) approximately every 4 floors. Using 2×2 jumper plates I was able to taper the model by just one stud (half stud on each side) every 2 floors. This definitely minimized the jaggedness and resulted in a smoother taper.

However, there is one downside to using half stud offsets and this became apparent on the model of the Transamerica Pyramid. The pyramid of this building is flanked by “wings” on two sides which are structures that hold the elevator shaft and stairwell. In my model, the wings needed to rise vertically without any tapers and this meant I would have normal wall sections intersecting the pyramid walls that are tapered using half stud offsets. In this situation, half stud gaps are unavoidable (because the bricks that make up the tapered pyramid are no longer in a straight line vertically). As you can see in the picture below, I did my best to plug these gaps by attaching tiles to the “wings”.

Tapering by unequal amounts in the two dimensions

My LEGO model of the John Hancock Center in Chicago presented a different kind of challenge. In order to accurately represent the proportions of the real building, I needed to taper the wide and the narrow sides of the model by different amounts in terms of studs. So I couldn’t simply use the 2×2 jumper plates like I did on the Transamerica Pyramid. I had to use a mix of 1×2 jumper plates (oriented two different ways) along with 2×2 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).

To help illustrate this a little better, I have created a simplified example where I taper a building with 12 floors from a base that is 8×6 studs to a top that is 3×3 studs. The longer side goes from 8 studs to 3 studs in 6 steps (and so it needs to be tapered by a stud every 2 floors). The shorter side goes from 6 studs to 3 studs in 4 steps (and needs to be tapered by a stud every 3 floors).

Here’s a breakdown showing the offsets needed (or not) at each floor to achieve this unequal taper in the two dimensions (X and Y).

Other uses of jumper plates

One other interesting thing about jumper plates is that they have “open” studs that allow plates and bricks to be attached on the top without any offsets. So why even bother using jumper plates ? The answer is “clutch power” or the ability of a LEGO piece to hold together tightly to the piece it is attached to. Given that a 1×2 jumper plate has just 1 stud on the top and two anti-studs (or receptacles for studs) on its underside, means that it has higher clutch power on the bottom than it does on the top. This makes it very useful in big models that have multiple sections that need to be put together and taken apart easily. The jumper plate tends to stay attached firmly to the layer below it while allowing the layer above to be separated without much effort. I tend to mix in jumper plates with tiles at the seams between the different sections that make up my skyscraper models (and I have never had to worry about loose pieces coming off while taking the sections apart).

Here’s an example showing the seam between the base in my model of the Empire State Building and the section above it. You can see a sprinkling of jumper plates among the tiles and these allow the section above to be held in place but separated from the base easily.

SNOT with half stud offsets

This SNOT technique doesn’t use jumper plates but I decided to include it here anyway. It makes use of the Technic 1×2 brick with 1 hole (part 3700). You can insert a Technic pin (part 4274) in the hole to create a “stud” and then use SNOT to attach tiles and other elements to the faces of the Technic 1×2 bricks. The tile is essentially offset by half a stud relative to the stud locations on the Technic bricks and helps add subtle detail.

You can see this technique used in the top section of my model of the Empire State Building along with some of the other techniques we covered earlier.

So the next time you build something using LEGO, don’t underestimate those lowly jumper plates. You just don’t know when or where they may come in handy. If you have any other applications for jumper plates that I have not covered here, please feel free to post a comment. Happy Building !

(Note: This is an expanded version of an earlier post – this time all the pictures have also been redone).

Thinking Outside the Grid – Building Angled Walls using LEGO


How many different ways can you attach a 1×6 brick to a baseplate ? There are quite a few as you can imagine, but each time the studs of the brick have to line up with the studs of the baseplate under it. That is just how LEGO works. The studs on the baseplate are in a regular square grid and therefore you can only place your 1×6 brick such that it is parallel to one of the sides of the baseplate. Suppose you are building a castle out of LEGO and one of your walls needs to be at a 45 degree angle, are you out of luck ?

Remember the regular square grid I mentioned earlier ? If you take any stud on the baseplate, it is exactly the same distance away from each of its neighbors on all 4 sides and that distance happens to be 0.8 cm (or a “stud” which is also the basic unit of measurement in LEGO). But the studs in the 4 corners are farther away (the distance is √2 x 0.8 cm = 1.414 x 0.8 cm = 1.13 cm to be exact). That is because in a square, the 4 sides are of equal length but the distance between any two opposite corners is a little longer. Similarly, the distance between any two studs measured at any angle other than 0 or 90 degrees is not guaranteed to be a whole number of studs.

So how can we turn our 1×6 brick to a different angle and still have it attach firmly to the baseplate ?

Angled wall basics

Let’s try a little experiment now – place two 1×1 plates as shown in the picture below. Now, if you place the 1×6 brick diagonally bridging these two 1×1 plates, it works ! The studs at the two ends of the 1×6 brick line up with the studs on the two 1×1 plates. This allows the 1×6 brick to have a good connection to the baseplate (at least at the two ends). The remaining 4 studs on the 1×6 brick still don’t line up with the studs below (now you see why we had to use the 1×1 plates as spacers to raise the 1×6 brick). So what exactly is going on here ?

If you jog your memory back to high school math (if you haven’t gotten there yet, you will just have to take my word for it), the equation a2 + b2 = c2 may seem vaguely familiar. That is the Pythagorean Theorem that defines the relationship between the sides of a right angled triangle.

Let’s take a closer look at where the two 1×1 plates were placed on the baseplate. If we count along the two sides of the baseplate starting from the corner, we see that the 1×1 plates are 3 and 4 studs away from the corner stud and make up two sides of a right angled triangle. Our 1×6 brick is placed along the third (and longest) side, also known as the hypotenuse. The triangle we created satisfies the Pythagorean theorem because 32 + 42 = 9 + 16 = 25 which is equal to 52. Then, does it make sense that we used a 1×6 brick for the longest side ? Yes, because the three sides of the right angled triangle intersect at the studs and the distance that really matters is the distance between the studs at the two ends of the 1×6 brick which is 5 studs.

So the bottom line is that for any brick or plate to be placed at an angle other than 0 or 90 degrees, you need to make sure the resulting triangle satisfies the Pythagorean theorem. Any set of 3 numbers that satisfies this theorem is called a Pythagorean triple and (3, 4, 5) is the smallest such set made up of whole numbers. What are some other Pythagorean Triples ? Listed below are all the Pythagorean Triples with numbers less than or equal to 25. As you can see, there are not many with practical applications in LEGO builds.


Angled walls using hinge elements

If we were to use the method described earlier to build angled walls, there is just no good way to avoid gaps at the corners where the angled wall segments meet the regular wall segments placed along the LEGO grid. An alternative is to use hinge elements.

There are many different types of LEGO hinge elements but the ones we need for angled walls are the ones that swivel – specifically the 1×4 hinge plate that consists of a 1×2 swivel base and a 1×2 swivel top.

The 1×2 plates that make up each of the two halves of the hinge plate are joined at their corners by a hinge that allows the angle between the plates to be changed from 0 to 180 degrees. If you place two 1×4 hinge plates as shown below, you can bridge them with a 1×5 plate (yes, LEGO makes one now !) attached at the top.

We are still creating the same right angled triangle (3, 4, 5) as before, but this time the hypotenuse (angled side) has 5 studs instead of 6. This is because the sides of the right angled triangle now intersect at the corners of the plates rather than the studs.

When close enough is good enough

The angled wall we built earlier can probably pass for a 45 degree wall but if you take a closer look at it, the smaller angle is more like 37 degrees. A right-angled triangle with a 45 degree angle is called a special right triangle because the third angle also ends up being 45 degrees (the three angles in a triangle have to add up to 180 degrees). This also means that the two sides that make up the right angle have to be of equal length. None of the Pythagorean triples we have seen, has two smaller numbers that are equal. So is it really possible to achieve a 45 degree wall using LEGO ?

Thankfully, the little bit of give that hinge plates have, allow us to use numbers that are close enough to Pythagorean triples. Consider for instance (5,5,7) and (7,7,10) which are “near triples” that allow you to build LEGO walls at 45 degree angles as shown below.

(12, 12, 17) and (17, 17, 24) are a couple of others. There are also “near triples” like (4, 7, 8) and (4, 8, 9) that don’t give you a 45 degree angle but are useful nonetheless.

Using jumper plates for even more options

Pythagorean triples (or “near triples”) also work when you multiply all the numbers in a triple by a whole number like 2 or halve them. For instance, take the triple (3, 4, 5) and multiply all the numbers by 2 and you get another triple (6, 8, 10). Similarly, if you take the “near triple” (7, 7, 10) and halve all the numbers, there is reason to believe that (3.5, 3.5, 5) would work. But how do you create a triangle that has sides that are 3.5 studs long ? Using jumper plates, of course !

Combining “near triples” with half stud increments gives you more options for building 45 degree walls. One combination I have found to be particularly useful is (8.5, 8.5, 12) which is half of a “near triple” (17, 17, 24).

Angled Walls – Hearst Tower

The Hearst Tower in New York is a wonderful example of a skyscraper that combines old and new architectural styles. It preserves the façade of the original 6-story Art Deco building as its base and adds a modern glass tower on the top. Two of the corners of the base are chamfered and I needed to build 45 degree walls for those two corners. Based on the scale I was using, I needed the angled wall section to be about 7 studs wide. This was a perfect application for the “near triple” (5,5,7).

Angled Walls – Taj Mahal

One of the modern wonders of the world, the Taj Mahal in Agra, India is probably one of the most well known masterpieces of Islamic Architecture. The main structure in the Taj Mahal is a mausoleum that sits on a raised platform. The mausoleum is shaped as a cube with four truncated corners that create the shape of an unequal octagon. To create the chamfered corners in my LEGO model, I used another “near triple” (7, 7, 10).

Angled Walls – Tribune Tower

One of the most beautiful skyscrapers in the world – the Tribune Tower in Chicago was inspired by Neo-Gothic architecture. Its highly ornate crown complete with flying buttresses was designed after the Butter Tower of the Rouen Cathedral in France. My LEGO model of this building required not one but several different types of angled walls. For the chamfered corners of the main tower I used the “near triple” (5,5,7). The two levels of the octagonal crown used two near triples – (8.5, 8.5,12) and (7,7,10) and the flying buttresses were attached to the base of the crown using another near triple (4,7,8).

Angled walls using the “switched diagonals” technique

This article would not be complete without at least a mention of another way of creating angled walls using LEGO. I have not personally used this in my models but it is still good to know and have in your toolkit.

The diagonal distance between two studs on a plate may not be a whole number of studs. But if you take a rectangular plate, the distances between the two pairs of studs at opposite corners (1, 3 and 2, 4) are exactly the same. So you can rotate the plate and attach it such that its corners 2 and 4 line up with where the corners 1 and 3 normally would be. Once again you will need to use 1×1 plates as spacers.

If you think of 1-3 and 2-4 as the longest sides of two identical right angled triangles that are mirrored, all you are doing is rotating one of the triangles so that the longest sides are lined up. The angle of rotation would obviously depend on the size of the right angled triangle (the number of studs on the two sides that make up the right angle). It turns out that the closest you can get to a 45 degree rotation is by using a 4×8 plate.

This technique can also be extended to include hinge elements. It looks a little different because this time the diagonals that are switched go all the way to the corners of the plates.

I am sure there are several other ways to create angled walls that I have not been able to cover here – using Technic elements, turntables and so on. I am hoping the overview I have provided at least points you in the right direction for your own exploration of these techniques. Please let me know if there are other techniques you have used that merit an inclusion here. Happy building !

(Note: This is an expanded version of an earlier post – this time all the pictures have also been redone).

Squaring the Circle – Building Round Shapes using LEGO

LEGO is not a medium that is inherently suited to building round shapes. After all, the basic building block – a 1×1 brick has a square footprint and a LEGO baseplate has studs placed in a regular square grid. And yet, there are many wonderful LEGO creations out there that include round shapes – all kinds of cylinders and even spheres. I did not have much experience building these shapes out of LEGO until I started working on my own version of the Taj Mahal. The focal point of this well-known landmark (which happens to be one of the modern wonders of the world) is its massive dome which sits atop a cylindrical base called the drum (that is an actual architectural term !). The minarets (slender towers) that sit at the 4 corners of the plinth of the Taj Mahal are essentially stacked cylinders too.

Needless to say, I had to take a deep dive into all the techniques out there that can be used to create round shapes using LEGO – I basically scoured the web looking for any information I could find on this topic. Every step of the way, I was amazed and inspired by the endless creativity of the AFOL community (I also tapped into some of the tools created by the Minecraft community). While I can’t claim to have invented any of the techniques listed in this article, I am happy to catalog them here for future reference (giving credit to the inventors wherever possible).

So what exactly is involved in creating round shapes out of LEGO ? The title of this post refers to “squaring the circle” which is an age-old mathematical problem that people tried to solve for centuries until it was proven (in 1882) to be impossible to solve. However it is possible to get close enough by using an approximation of the number π (pi). In much the same way, all the techniques described here try to use square/rectangular bricks or plates to create the best approximation that is possible of the round shape. The result is never perfect and the limitations of the LEGO medium are always apparent in the jaggedness of the curves and the gaps that you may see, especially when you are looking at your model up close. But the trick is creating a pretty convincing illusion of a round shape at least when you look at your model from a few steps back.

1) Using SNOT to create small cylinders

For the minarets of the Taj Mahal, I did not want to be limited by the small selection of cylinder pieces that LEGO has. I wanted to try a different way of building cylinders that could be scaled to whatever height I needed. I was already familiar with using curved slopes and SNOT to create round shapes (I had used this technique to build the crown in my model of the Chrysler Building). The same technique can be used to create cylinders with various diameters. All the cylinders in the picture below can be built in height increments of two studs.

The smallest cylinder was just right for the minarets of the Taj Mahal, based on the scale I was using. Ideally the minarets should taper as they rise – the way they do in the real Taj Mahal. Unfortunately there was no easy way to reduce the diameter of the smallest cylinder any further.

2) Bending LEGO walls to create round shapes

A “brute force” way of building round walls using LEGO is by building straight walls and then bending them to form a circle. The longer your wall, the more flex it will have, making it easier for you to bend it into a complete circle. The number of 1×2 bricks needed in each layer to build a stable round wall tends to be around 72, give or take a few bricks. But I have seen round walls built using far fewer plates in each layer.

Check out the work of Jeff Sanders who specializes in “brick bending”. He has an impressive portfolio of creations, made by bending LEGO brick walls not just into circles but various other shapes as well.

Please note that most brick bending techniques are illegal, strictly speaking, because you are using LEGO elements in ways they are not intended to be used and subjecting them to undue stress and possible damage. An obvious downside to this technique (other than it being illegal) is the fact that it cannot be replicated digitally in

A few years ago, I embarked on a LEGO project unlike any other that I had worked on before. I wanted to try doing a studs-up mosaic in a round shape. I came up with my own pattern of intertwined snakes and used a little over 14000 plates to build this round thing that I like to think of as some kind of a vase (because a trash can isn’t as appealing). This sits in a corner somewhere in my basement because I still haven’t figured out a good way to finish this and create something worth displaying. Any suggestions would be welcome, of course !

3) Mixing regular bricks with round 1×1 bricks to create round walls

This uses the same approach as above – except for the fact that we use 1×1 round bricks (or plates) in our wall to allow it to be bent more readily (and legally !). If we alternate say 1×3 bricks in our wall (1×2 bricks also work) with 1×1 round bricks, the round bricks act like hinges to some extent, allowing the wall to be bent to form a circle. This method allows round walls to be built with smaller diameters than is possible with the previous method. The only downside is that the texture of the wall is uneven due to the 1×1 round bricks. It is possible to use tiles to hide the round bricks and create the effect of a real brick wall (credit goes to Steve DeCraemer on Flickr). The 1×3 bricks here are replaced with 3 headlight bricks with their top studs facing out. These headlight bricks are joined together with a 1×3 plates while 1×4 tiles are attached to the face of the round wall creating the look of a brick wall (which should work great for castle builds).

4) Round walls using hinge bricks/plates

We have seen that hinge pieces can be very useful for creating angled walls and various polygons (hexagons, octagons, etc). The greater the number of sides in a regular polygon (one where all sides have the same length), the closer it starts to approximate a circle. We can take advantage of this fact to use hinge pieces to create round walls.

One tutorial I came across on this topic is this one by Eggy Pop (flickr user name) –

I have re-created the round wall shown in this tutorial in using 14 1×4 hinge plates to complete the circle (which is essentially a polygon with 28 two-stud wide sides). One of the neat things about this particular round wall is that its diameter (18 studs on the inside, 20 studs on the outside) is a whole number in terms of studs. As you can see, the hinge plates on 4 sides line up with the LEGO grid allowing the round wall to be attached firmly to a base. So what is special about the number 18 ? Let us see if we can use some math to figure that out. Assuming the inside of the wall is close enough to a circle, its circumference would be the diameter times π (pi) = 18 x 3.14 = 56.52 studs. Now divide that by 4 (the length of a 1×4 hinge plate) and you get 14.13 which is close enough (for practical purposes) to a whole number 14 – which happens to be the number of hinge plates we used.

Don’t count on the same working for round walls with inner diameters of say 17 or 19 studs. What are some other numbers that work ? The two numbers closest to 18 that work are 14 and 23 (I used 23 for the drum in my Taj Mahal). As you can see from the pictures, these two numbers don’t work as well as 18 and the hinge plates on only 2 sides line up with the LEGO grid (which is usually good enough). Can we explain why ? In the case of 14, the number of hinge plates needed is (14 x 3.14) / 4 which is approximately 11. Since the number of hinge plates is not an even number, you don’t have the hinge plates lining up with the LEGO grid on all 4 sides. In the case of 23, the diameter itself is not even. And so, if you line up the hinge plates with the grid on one axis, the other axis is offset by half a stud (you could use jumper plates to attach the round wall to the base on the other two sides if needed).

Once issue with round walls is that when you have just 2 or 4 connection points to the base, the rest of the hinge plates are free to move and so the round shape can easily get distorted. There is no elegant solution I could think of, to get the wall to maintain its shape (I guess you could use long plates as cross members joining each side of the polygon to the one on the opposite side and then have these cross members attached in the middle using turntables). For now, I just built a regular inner wall as close as possible to the round wall, and attached cheese slopes, curved slopes, etc. to the inner wall using SNOT to fill the gaps the best I could. Since the drum has an outer diameter of 25 studs and I needed to center it on a 24×24 base, I ended up using jumper plates. I also needed jumper plates to center the dome (which is built with a core that is 16×16 studs) on the top of the drum.

While it is quite straight-forward to build these round walls using real pieces, how do you do it in ? The hinge tool allows you to select a piece and rotate it around a hinge point. In this case, the piece being selected would be one half of the 1×4 hinge plate. When you click on the piece with the hinge tool enabled, you will first see a blue arrow. You can click and drag this blue arrow to manually rotate the piece. Or you can click on the blue arrow to get a white text box where you can enter the precise angle to rotate the piece by.

With round walls it is important to make sure all the hinge plates are rotated by just the right amount or the two ends of the wall will not line up correctly to allow you to complete the circle. To figure out the right angle to use, just divide 360 by the number of sides of the polygon you are building which in the case of the first circle (18 studs diameter) would be the number of hinge plates times 2 = 14 x 2 = 28. 360 divided by 28 is 12.85 degrees which is the number you need to enter in the text box. I tend to apply this rotation to one hinge plate and then copy and paste the hinge assembly (both halves together) as many times as I need.

One tip regarding the use of hinge plates in – in order to be able to rotate the hinge you need to use the two separate halves that make up the hinge plate (the swivel base and swivel top). However, when it is time to place your Bricklink order(s) and you upload the parts list from, be sure to edit your wish list to replace the two halves with the complete hinge assembly. The hinge assembly (both halves together) tends to be way cheaper than buying the two halves separately.

5) Building spheres by stacking regular bricks or plates

To understand how spheres are built using LEGO bricks, I have found it useful to first look at the world of Minecraft. There are some parallels between Minecraft and LEGO in that both use building blocks with square footprints that are placed on a square grid. One important difference is that the blocks in Minecraft are perfect cubes while a basic 1×1 LEGO brick is not (it is taller than it is wide). More on that later. Anyway, there are a number of resources available in the Minecraft community for building spheres and other shapes using Minecraft blocks and I was wondering if I could leverage some of them for building LEGO spheres.

Before we look at a 3-dimensional sphere, let us look at a basic circle in 2 dimensions. Minecraft enthusiasts often use what is known as a circle chart. It shows the placement of blocks (or pixels) in a square grid that best approximates a circle. The chart shows circles with different diameters and as you can see from the chart, the bigger the diameter, the more convincing the illusion of the round shape is.

Minecraft circle chart

In the Minecraft world where the building blocks are perfect cubes, you can also look at one of the circles and think of it as the side view of a sphere. You can think of each row in the chart as one of the layers of blocks in the sphere you are building. So you would essentially start with a layer of blocks placed in a circle having the diameter of the sphere you want to build (that would be the biggest circle you need). You would then stack layers with successively smaller circles (as you go up) until you reach the smallest circle you need. Repeat the same on the bottom (with the circles getting smaller as you go down) and you have a complete sphere. Of course, it could be a lot of work to figure all this out by hand (even with the help of a circle chart). Thankfully, an online tool (Plotz Sphere Generator) can automate this process for you. You just enter the diameter you need and presto, a sphere is generated for you (with 3D and 2D views showing how the sphere is constructed layer by layer).

That sounds simple – right ? Unfortunately, there is a lot more work involved if you want to build this sphere using LEGO bricks. For one, the sphere generator just shows blocks which are equivalent to 1×1 LEGO bricks but you know these bricks just can’t be stacked the way you see in the 3D view. You need to convert the 1x1s into longer bricks that form an interlocked structure that holds together well. You also need to make the walls of the sphere at least 2 studs deep, allowing each successive layer (which is a smaller circle as you move away from the middle layer) to rest on the layer immediately below it. There is one last hitch – if you replace all the blocks in the Minecraft sphere with 1×1 LEGO bricks you will not end up with a perfect sphere. Your sphere will be a little taller than it is wide – just like a 1×1 brick. Thankfully there is also a Plotz Ellipsoid Generator available on the same site and you can use that and compensate for the shape of a 1×1 brick.

For the sphere I built using LEGO bricks, I used Plotz to create an ellipsoid with a width and depth of 36 units and a height of 30 units. Why did I pick a shape that is a little squat compared to a perfect sphere ? Notice that the ratio of height to width of the ellipsoid is 5/6 which is the inverse of the proportions of a 1×1 LEGO brick (which has a height to width ratio of 6/5). And so when we use LEGO bricks which are taller than they are wide, the proportions even out and we end up with a perfect sphere.

The sphere looks good but it is a little blocky. Is there a way to smoothen the curves – perhaps by using LEGO plates which are 1/3rd as tall as bricks ? We go back to the Plotz Ellipsoid Generator and this time the numbers we use have to reflect the shape of a 1×1 LEGO plate with a height to width ratio of 2/5. I used a height of 50 units and a width of 20 units which gives us a height to width ratio of 5/2. This way when we replace the Minecraft blocks with 1×1 LEGO plates (combined into longer plates as needed) we get a perfect sphere. Looking at this sphere from the side, we can see a definite improvement compared to the earlier sphere. The curves are much smoother thanks to the smaller gradations achieved by using plates instead of bricks. But the limitations of this approach are quite apparent when you turn the sphere and look at it from the top. From this view, the curves once again appear blocky. As it turns out, using plates to build the sphere only makes the curves smoother in one of the three dimensions. Another downside to spheres built by stacking bricks or plates is that the undersides of the bricks and plates are visible when you look at the bottom side of the sphere.

Is there a way to achieve smoother curves in all 3 dimensions without any of those pesky undersides of plates being visible ? If we could take just the top part of this sphere that is smoother and somehow use it in all 3 dimensions (all 6 sides), we would have a sphere that looks smooth all around – correct ? That is exactly the idea that AFOL extraordinaire Bruce Lowell had back in 2002. His invention sort of revolutionized the construction of round shapes (not just spheres) using LEGO, earning him the distinction of being the only AFOL (I know of) to have a building technique named after him – the Lowell Sphere !

6) Lowell Spheres

A Lowell sphere consists of a SNOT cube (with studs in all directions) with 6 identical curved panels (built using LEGO plates) attached on all 6 sides. Each panel is longer than it is wide allowing the 6 panels to interlock perfectly without any visible gaps. Bruce Lowell’s original Lowell Sphere had a diameter of 6.8 studs and it had an inner core that was 4x4x4 studs wide. But in the years that followed, this technique has taken on a life of its own, finding applications in not just spheres but other complex sculptures as well.

While the original 6.8 stud wide sphere is pretty easy to figure out, how do you apply this technique to build bigger spheres ? Another AFOL who has been key to making this technique accessible to everyone is Bram Lambrecht. He developed Bram’s Sphere Generator which allows you to create a Lowell Sphere with any diameter that you need. Just enter the diameter (in increments of 0.2 studs), tweak a few settings and you are ready to save a Ldraw file that can be imported into There is an option to use half stud offsets (jumper plates) to get more detail but I have not found that to be practical for larger spheres. One very useful setting is “use alternating layer colors” and with this selected, different colors are used for the layers of plates that make up each of the 6 identical panels. You may wonder why that is useful. The Ldraw file has sub-models for the 6 panels. But when you release (ungroup) one of these sub-models, you will see that each panel is built entirely out of 1×1 plates. So there is some work involved here, going layer by layer and replacing the 1×1 plates with bigger ones. You have to pick the plates in such a way that the entire panel holds together as one unit (by ensuring that the seams between plates don’t line up between successive layers). The good news is that once you have worked on one panel, you can save it back as a sub-model and use that for all the 6 sides. The Ldraw file also doesn’t include the core and so you will have to build that as a SNOT cube with studs in all 6 directions (just a handful of connection points for each of the 6 panels is usually sufficient).

For the rounded dome of the Taj Mahal, I created a Lowell Sphere with a diameter of 27.2 studs. This is made up of a core that measures 16x16x16 studs and 6 curved panels that are each 14 plates thick (so the diameter is 16 studs + 28 plates which is equivalent to 16 + 11.2 = 27.2 studs). Clearly, I didn’t need the bottom part of the sphere and so I had to truncate it. I ended up removing the bottom panel of the sphere entirely and reducing the height of the core by 2 studs to 14 studs. I also had to crop the bottom portions of the curved panels on the 4 sides (since the panels are oriented two different ways, I had to create two variants of the cropped side panels). The bottom portion of the dome which sits on the drum ended up having a diameter of 16 studs + 22 plates = 24.8 studs which was very close to the outer diameter of the drum (25 studs).

The concept of the Lowell Sphere can be extended to other shapes. Lsculpt also developed by Bram Lambrecht, allows you to convert a 3D model into a LEGO sculpture that is structured much like a Lowell Sphere with a SNOT core (that is not necessarily a cube) that has curved panels attached in all 3 dimensions. Here’s a heart sculpture that I built digitally using Lsculpt.

There are several other ingenious ways of creating round shapes using LEGO that I have not been able to cover here. I am hoping that this post at least gives you a starting point for your own exploration into some of these techniques. I would welcome any questions or suggestions that you may have. Happy building !

LEGO Building Techniques – Angled Walls

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

If you look at a LEGO baseplate, you will see that the studs on it are arranged in a regular grid with any two neighboring studs exactly 0.8 cm apart (measured center to center). However, this is true only if you are measuring the distance parallel to one of the sides of the baseplate. If you were to measure the distance between two studs that are next to each other diagonally, the distance would be slightly longer (√2 x 0.8 = 1.414 x 0.8 = 1.13 cm to be exact). Herein lies the problem – you can place bricks every which way on the baseplate as long as they are parallel to one of the sides of the baseplate. But as soon as you turn the bricks to an angle different from 0 or 90 degrees, the studs no longer line up.

The trick to placing bricks at a different angle (with good stud connections at both ends) is making sure the triangle you form satisfies the Pythagorean Theorem. Most people haven’t encountered this since high school math, but it basically states that in a right angled triangle, a2 + b2 = c2 where a and b are the adjacent sides that make up the right angle and c is the hypotenuse (or the longest side that is opposite to the right angle). The smallest Pythagorean triple (set of 3 numbers that satisfy the theorem) is 3, 4 and 5 (and that is because 32 + 42 = 9 + 16 = 25 which is equal to 52).

How does this Pythagorean triple (3, 4, 5) translate to LEGO ? Basically, if you place your brick or plate at an angle such that it forms a triangle (3 studs long on one side and 4 studs long on the other), then the studs at the two ends of your brick or plate (but not the ones in the middle) will line up perfectly with the studs directly below. Then, does it make sense that we are using a 1 x 6 plate in the first picture ? Yes, when you consider the fact that the sides of our triangle actually intersect at the centers of the studs, the distance that matters is between the studs at the two ends of the 1 x 6 plate which is 5 studs. The same applies to the other two sides. However, when we use hinge plates to create our triangle, the longest side has 5 studs instead of 6 (because the sides of the triangle now intersect at the corners of our plates).

What are some other Pythagorean triples ? 5, 12, 13 is the next one before we get into much bigger numbers that are not very useful. If we limit ourselves to Pythagorean triples, there are not many to pick from (especially with practical applications in LEGO builds). But if we use LEGO hinge plates to build our angled walls, the little bit of give that these have, allow us to use triples that are not Pythagorean triples (strictly speaking) but are close enough. Most angled wall applications call for the walls to be at 45 degree angles which means the two sides (a and b) of our triangle have to be of equal length. There are no Pythagorean triples where a and b are equal but there are many that are close enough. Consider for instance 5, 5, 7 and 7, 7, 10.

I happened to use 5, 5, 7 to create the angled corners in the base of my model of the Hearst Tower.

Pythagorean triples also work if you multiply all the numbers by 2 or halve them. If you use 7, 7, 10 as an example of something close enough to a Pythagorean triple, then 14, 14, 20 and 3.5, 3.5, 5 should also work. But how do we create a triangle in LEGO with 3.5 studs on its side ? Using jumper plates, of course !

I used angled walls extensively in my model of the Tribune Tower. Here the main tower used 5, 5, 7 for the angled corners. For the octagons in the crown, I used 7, 7, 10 (for the smaller one) and 8.5, 8.5, 12 (for the bigger one) to create the angled sides. The flying buttresses also needed to be attached at an angle (though not 45 degrees) and for that I used another triple that was close enough – 4, 7, 8.

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.