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.
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).