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...
yeah. I think his website is extremely old and hasn’t been updated in the last decade or so. Despite this I linked to it because he is a legend in this field and so i think this is still the definitive reference.
As far as i understand, part of the story as to why dodecahedron and the cube fall short is due their non-triangular faces.
Did the article switch the dodecahedron and icosahedron? It specified that the icosahedron is optimal for 12 points and the dodecahedron for 20 which seems backwards to me.
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.