Talk:Snub 24-cell

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Untitled[edit]

That wasn't an error. 0:1:φ:φ2 is equivalent to 0:φ-1:1:φ. If you prefer the latter, you should also change the edge length to 2/φ (which I find inelegant which is why I used the first form of the coordinates). —Tamfang 16:35, 17 February 2006 (UTC)


It's not my place to revert it to my own version, but ... Is the ambiguous term "snub octahedron" really necessary when the sentence expressly mentions the octahedron? —Tamfang 16:39, 17 February 2006 (UTC)

Hilariously, "snub octahedron" could mean the icosahedron, the snub cube, or even the compound of four octahedra! 4 T C 13:42, 5 February 2010 (UTC)

projection[edit]

Whatever the green figure is, it certainly isn't a stereographic projection, which would have curved edges and faces. —Tamfang 21:49, 6 January 2007 (UTC)

I agree the terminology is unclear, and I prefer Schlegel diagram, but I would say Stereographic projection applies if the vertices are mapped spherically, while the edges are drawn linearly. Tom Ruen 23:33, 6 January 2007 (UTC)

"stellation"[edit]

Conversely, the 600-cell may be constructed from the snub 24-cell by stellating it with 24 icosahedral pyramids.

Stellation usually means extension of existing facets in their respective hyperplanes, which this clearly isn't. —Tamfang (talk) 17:45, 1 October 2008 (UTC)

It's more along the lines of Conway's kis operator than a stellation in the sense of a non-convex regular polytope.—Tetracube (talk) 23:51, 20 October 2008 (UTC)
By Johnson terminology, the term is Augument, like augmented triangular prism. kis is okay too, but more of a topological than geometric operation. Tom Ruen (talk) 00:09, 21 October 2008 (UTC)
OK, I like augmented. I'll update the article.—Tetracube (talk) 02:36, 21 October 2008 (UTC)
What about "cumulated"? Professor M. Fiendish, Esq. 07:43, 9 September 2009 (UTC)
What does that mean?—Tetracube (talk) 17:21, 9 September 2009 (UTC)
Mathworld has the term at [1], looks like the Conway kis operator. Tom Ruen (talk) 18:08, 9 September 2009 (UTC)

Width=640[edit]

Hi Tom Ruen,

Is there any particular reason you changed the table in Projections to have width=640? It looks very ugly on my browser because I use large fonts on a high-resolution screen, and forcing the table to be 640 pixels causes too many word-wraps. Does Wikipedia have any guidelines on pixel-widths? In general, I find websites that use pixel widths to render very uglily on my browser because they assume a particular font size (and using that font size will make the text unreadably tiny on my screen). Could we please just let the browser decide how to lay out the table?—Tetracube (talk) 18:36, 14 January 2009 (UTC)

I thought it looked better to balance narrow pictures and narrow paragraphs, but that's my default IE fonts. I can imagine a larger font would format poorly. How about putting the text below each picture? Again, maybe won't help you? Tom Ruen (talk) 18:51, 14 January 2009 (UTC)
I suppose we could, although I thought the whole point of using a table-based layout was so that the text could run alongside the image.—Tetracube (talk) 22:36, 14 January 2009 (UTC)
OK, the double-column format works, too. Thanks.—Tetracube (talk) 06:50, 15 January 2009 (UTC)

does every projection have a center?[edit]

Orthogonal projection — Centered on hyperplane of one icosahedron.

I suspect this means to say the projection is into such a hyperplane. If not, I can't guess what the "center" of an orthogonal projection might be. —Tamfang (talk) 06:24, 15 January 2009 (UTC)

Looks to me to be a projection centered on an icosahedron. Not sure why it was worded in such an awkward way ("centered on hyperplane of one icosahedron"---does a hyperplane have a center?). "Centered" here simply means that the 4D viewpoint is oriented such that the icosahedron in question projects to the central region of the image. Compare, e.g., a vertex-centered projection (image has vertex in question projected to the center of the image) vs. a face-centered projection (the face in question projects to the center of the image, IOW the center of the face projects to the center of the image).
In any case, the hull of the projection image is consistent with the icosahedron-centered orthogonal projection of the snub 24-cell.—Tetracube (talk) 06:48, 15 January 2009 (UTC)
A hyperplane doesn't have a center, but if it passes through the center of a figure it's only slightly sloppy to say it is a center, and thus can have something centred on it. But that's beside the point ...
If an orthogonal projection (of a uniform polytope) brings a given facet to the center of the image, then the hyperplane of the image must be parallel to that of the facet, no? —Tamfang (talk) 20:53, 19 October 2009 (UTC)
True. In that case, we should say something to the effect that the direction of the projection is orthogonal to the hyperplane of the facet. It doesn't make sense to say that it is centered on a hyperplane---a hyperplane can't be the center of anything since it's not a point.—Tetracube (talk) 21:45, 19 October 2009 (UTC)
Definitely could use improving. What it MEANS is the icosahedron cell DEFINES the 3D hyperplane of the 3D orthogonal projection, i.e. ignoring one basis direction perpendular to the cell. It is also true that this projection leaves the icosahedron in the center of the 3D projection. Tom Ruen (talk) 22:59, 19 October 2009 (UTC)
Here's the projection with only the "central icosahedron" visible. It is an orthogonal projection from 3d to 2d also, and centered on a face, so lots of overlapping vertices/edges.
Snub 24-cell ortho icosa.png