Good article, but it'll take some time to understand it. %1 is interesting, I used to use {..} for taking fractional part, %1 is intuitively easy, though not looking particularly good...
Regarding the two-variable function mod(x,b). Typically this is written as x (mod b) in maths, and as x%b in computing.
It is generally well known that for positive integers x and b, the output of this function is the remainder when x is divided by b.
However, what is less well-known is that if b=1, then the convention is that:
x (mod 1) = x%1 = fractional part of x.
For example, Python, Excel both implement this special convention.
As far as i understand, part of the story as to why dodecahedron and the cube fall short is due their non-triangular faces.
Icosahedron: 12 points, 20 faces (and 30 edges)
Dodecahedron: 20 points, 12 faces (and 30 edges)