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Lego dimensions: the measurements 
There are five basic dimensions:
As one can see, dimensions have even numbers after the decimal point.
These five basic dimensions are not "fundamental". Most dimensions are even multiples of 0.8mm.
Multiple of base  Value in mm  Meaning 
1  0.8  
2  1.6  
3  2.4  
4  3.2  plate thickness 
5  4.0  
6  4.8  axle diameter; knob diameter 
7  5.6  
8  6.4  two plates 
9  7.2  
10  8.0  horizontal pitch 
11  8.8  
12  9.6  vertical pitch; three plates 
13  10.4  
14  11.2  
15  12.0  
16  12.8  
17  13.6  
18  14.4  
19  15.2  
20  16.0 
All measures are even multiples of 0.1mm except where they are derived. E.g. the width of a brick wall will be 1.5mm:
8.0mm (basic pitch)  0.2mm (0.1mm play on each side)  4.8mm (size of knob) = 3.0mm = 2x wall thickness.

In addition there is:
All other measures are derived from these.
From this follows that normal bricks have horizontal dimensions that are multiples of 8mm, and then minus 0.2mm.
Examples:
4 knobs brick: 4x8  0.2 = 32.0  0.2 = 31.8 6 knobs brick: 6x8  0.2 = 48.0  0.2 = 47.8 … 16 knobs beam: 16x8  0.2 = 128  0.2 = 127.8 
A plate is 1/3 the height of a normal brick which therefore is 9.6/3 = 3.2
The other side of bricks:


The cylinders under the classic bricks provide extra hold on the knobs. Their diameter therefore is computed by:
These have the bearing holes for Lego axles. The smallest Technics brick has one knob and is special:


Normal Technics bricks have the holes in between the knobs:


[to come]