HUH???

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HUH???

Postby Neues Kinder » Sun Sep 25, 2005 4:40 pm

I've been browsing around the site, and I noticed that they name the 600-cell a hexacosichoron. What's the deal with that? Isn't that the name that you would give a 26-cell? Wouldn't a 600-cell be called a hexahectachoron or something?
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Postby wendy » Sun Sep 25, 2005 11:48 pm

The fifhundchoron {3,3,5} is also called by the greekish name hexacosichoron

hexa. 6

cosi. of teenty (ie 100 dec)

choron. 3patches

cosi is greekish reduction of hundred, in much the same way that ten -> ty, eg -tehun vs -tig.

W


ps, i use 'twelftychoron' for its dual {5,3,3}.

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Postby Neues Kinder » Mon Sep 26, 2005 8:48 pm

wendy wrote:The fifhundchoron {3,3,5} is also called by the greekish name hexacosichoron

What is meant by the Schoeffler numbers (or however you spell it)? I don't get how {3,3,5} can represent a 600-cell. I'm only in high school and I'm taking a Geometry course, so I don't know about that kinda stuff yet.

wendy wrote:cosi is greekish reduction of hundred

Oh, so the prefixes for 20 and 100 are almost the same. That's where I got confused, because the prefix for 20 is icosa. OK, I understand it now.

So what are the prefixes for 30, 40, 50, 60, etc.? Just so I know.
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Postby wendy » Mon Sep 26, 2005 10:49 pm

Schlafli symbol is a description for a figure. It works like this:

Code: Select all

  {p}  means a polygon
  {p,q}  means the faces are {p}, q at a vertex [margin]
  {p,q,r} means the faces are {p,q},  r at a edge [margin]



This means that for example, the {3,3,5} has triangle 2d-elements, {3,3} = tetrahedral faces, five at an edge.

You have, eg
    {3,3} = tetrahedron
    {3,4} = octahedron
    {4,3} = cube
    {3,5} = icosahedron
    {5,3} = cube

in 4d

    {3,3,3} = pentachoron = 5 tetrahedra
    {3,3,4} = 16choron = 16 tetrahedra
    {4,3,3} = tesseract = 8 cubes
    {3,4,3} = 24choron = 24 octahedra
    {3,3,5} = fifhundchoron = 600 tetrahedron
    {5,3,3} = twelftychoron = 120 dodecahedra
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Postby wendy » Mon Sep 26, 2005 10:51 pm

The greekish for 30 &c, are by using the -conta- infix, eg 'tricontahedron'

    tri = three
    conta = -ty
    hedron = faces


It is only twenty that is irregular.
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