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Lego dimensions: the basics |
Let us describe bricks in an orthogonal axis system: x and z axes lie in the horizontal plane, the y axis points upwards:
The figure shows a 2x4 red brick on a 6x10 yellow base plate, and a stack of three 2x4 plates.
In these pages we disregard the small influence that temperature has on the dimensions, we try to find the conceptual numbers that were used in the design of bricks (figuring out what the Lego engineers thought by looking at what they made instead of asking them is called reverse engineering).
The basic horizontal pitch is 8mm in both x and z directions. The vertical pitch is 9.6mm: the height of a normal classic brick. Plates are one third of that, or 3.2mm thick; it takes three plates to reach the height of a normal brick.
Because 8mm ≠ 9.6mm, the vertical and horizontal pitch are not the same, leading to problems (anisotropy).
To be able to build without too much friction, the sides of the bricks should not touch: there should be a little play (so to speak). This is achieved by a gap of 0.2mm in the horizontal plane between any two bricks. As the diagram below shows, this is done by moving all end faces 0.1mm away from the positions on the theoretical grid of 8mm pitch.
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The diagram is a top view of some red bricks on a yellow plate. The dotted grey lines are the 8mm grid. The reduction by 0.1mm is much exaggerated in order to show the effect. Because the sides of the plate are also moved by 0.1mm, its faces are flush with those of the red bricks. But the side faces of any two bricks placed side by side do not touch. Since all faces were moved by 0.1mm the gap between bricks is 2 x 0.1mm = 0.2mm
The smallest brick (one knob) is then not 8mm x 8mm but only 7.8mm x 7.8mm. A standard 2x4 knob basic brick should be 2x8=16mm wide and 4x8=32mm long, but it is actually only 15.8mm by 31.8mm. Any regular piece with a dimension of n knobs will be effectively nx8-0.2mm long in that dimension.
In general, this small gap can be ignored, since it does not accumulate in the building of a model.
There is no gap vertically (obviously).
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