Hacker News new | ask | show | jobs
by avmich 1750 days ago
This link - http://neilsloane.com/packings/index.html#I - has dead URLs. Like this - http://www.teleport.com/~tpgettys/dodeca.gif . I specifically wanted to check where the dodecahedron comes short.

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...

3 comments

You are right. In mathematics, the traditional notation {x} represents the fractional part of x.

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.

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.
I believe it is right. However, I often get these two intuitively mixed up because:

Icosahedron: 12 points, 20 faces (and 30 edges)

Dodecahedron: 20 points, 12 faces (and 30 edges)

Hmm, that explains it.
I know what dodecahedron is, I wanted to see the corresponding (by the number of vertices) maximally-separated polyhedron.
You cited a dead link. What I posted is the Internet Archive record of what was originally at that link.