How it works:
There is a section for each kind of element. Elements are divided by what they are connected to incidentally. That means one line segment may have two hexagons while another may have a square and a hexagon.
Lets take an example.
Dyad 1 - Square, 1 : Hexagon, 1 :
Here a line segment is connected to two kinds of faces, a square and a hexagon. But imagine within this polytope, there exists another kind of dyad bordering two hexagons. Here is how it would look.
Dyad 2 - Hexagon, 2 :
As you can see, the next to the face names, is the number of faces of that kind.
Now, let's get an example to see how this would work.
Colons divide each kind of element while slashes divide dimensions of elements.
Here's a couple of examples.
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Sirco
Square 1 - Square 2, 4 :
Square 2 - Square 1, 2 : Trig, 2 :
Trig - Square 2, 3 :
Dyad 1 - Square 1, 1 : Square 2, 1 :
Dyad 2 - Trig, 1 : Square 2, 1 :
Point - Square 1, 1 : Square 2, 2 : Trig, 1 : / Dyad 1, 2 : Dyad 2, 2 : /
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Squappy
Square - Trig, 4 :
Trig - Square, 1 : Trig, 2 :
Dyad 1 - Trig, 2 :
Dyad 2 - Square, 1 : Trig, 1 :
Point 1 - Trig, 4 :
Point 2 - Square, 1 : Trig, 2 :
I also have come up with some sort of graph which this notation is based on. Here it is.
Again, each element type is decided by what they are connected to and what they are.