4 ms·

This link - http://neilsloane.com/packings/index.html#I http://neilsloane.com/packings/index.html#I - has dead URLs. Like this - http://www.teleport.com/~tpgett

by avmich 5y ago

This link - http://neilsloane.com/packings/index.html#I http://neilsloane.com/packings/index.html#I - has dead URLs. Like this - http://www.teleport.com/~tpgettys/dodeca.gif 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...

zarang 5y ago
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.
- fiddlerwoaroof 5y ago
  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.
  - extremelearning 5y ago
    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)
    - fiddlerwoaroof 5y ago
      Hmm, that explains it.
sls 5y ago
https://web.archive.org/web/20000506214514/http://www.teleport.com/~tpgettys/dodeca.gif https://web.archive.org/web/20000506214514/http://www.telepo...
- avmich 5y ago
  I know what dodecahedron is, I wanted to see the corresponding (by the number of vertices) maximally-separated polyhedron.
  - sls 5y ago
    You cited a dead link. What I posted is the Internet Archive record of what was originally at that link.
extremelearning 5y ago
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.

by avmich 5y ago

zarang 5y ago

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.

fiddlerwoaroof 5y ago
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.
- extremelearning 5y ago
  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)
  - fiddlerwoaroof 5y ago
    Hmm, that explains it.

sls 5y ago

https://web.archive.org/web/20000506214514/http://www.teleport.com/~tpgettys/dodeca.gif https://web.archive.org/web/20000506214514/http://www.telepo...

avmich 5y ago
I know what dodecahedron is, I wanted to see the corresponding (by the number of vertices) maximally-separated polyhedron.
- sls 5y ago
  You cited a dead link. What I posted is the Internet Archive record of what was originally at that link.

extremelearning 5y ago

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.