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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).
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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
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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 Knowledge have any guidelines on pixel-widths? In
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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.
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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?—
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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
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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?
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That wasn't an error. 0:1:φ:φ is equivalent to 0:φ: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).
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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.
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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? —
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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? —
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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.—
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In any case, the hull of the projection image is consistent with the icosahedron-centered orthogonal projection of the snub 24-cell.—
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Whatever the green figure is, it certainly isn't a stereographic projection, which would have curved edges and faces. —
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Conversely, the 600-cell may be constructed from the snub 24-cell by stellating it with 24 icosahedral pyramids.
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usually means extension of existing facets in their respective hyperplanes, which this clearly isn't. —
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such a hyperplane. If not, I can't guess what the "center" of an orthogonal projection might be. —
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on
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a center, but if it passes through the center of a figure it's only slightly sloppy to say it
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a center, and thus can have something centred on it. But that's beside the point ...
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applies if the vertices are mapped spherically, while the edges are drawn linearly.
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operator than a stellation in the sense of a non-convex regular polytope.—
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Orthogonal projection — Centered on hyperplane of one icosahedron.
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is okay too, but more of a topological than geometric operation.
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599:18:08, 9 September 2009 (UTC)
568:17:21, 9 September 2009 (UTC)
546:07:43, 9 September 2009 (UTC)
347:16:39, 17 February 2006 (UTC)
337:16:35, 17 February 2006 (UTC)
278:and see a list of open tasks.
42:Put new text under old text.
808:22:59, 19 October 2009 (UTC)
787:21:45, 19 October 2009 (UTC)
764:20:53, 19 October 2009 (UTC)
735:06:48, 15 January 2009 (UTC)
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513:. I'll update the article.—
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50:New to Knowledge? Welcome!
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582:Mathworld has the term at
487:augmented triangular prism
362:compound of four octahedra
381:Hurrah for versatility. —
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80:Be welcoming to newcomers
531:What about "cumulated"?
419:Stereographic projection
391:22:15, 9 July 2023 (UTC)
310:project's priority scale
267:WikiProject Mathematics
197:This article is rated
75:avoid personal attacks
743:A hyperplane doesn't
558:What does that mean?—
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19:This is the
509:OK, I like
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609:Width=640
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515:Tetracube
511:augmented
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358:snub cube
88:if needed
71:Be polite
21:talk page
800:Tom Ruen
635:Tom Ruen
591:Tom Ruen
539:Fiendish
495:Tom Ruen
483:Augument
423:Tom Ruen
327:Untitled
56:get help
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27:article.
777:point.—
756:Tamfang
706:Tamfang
485:, like
448:Tamfang
405:Tamfang
383:Tamfang
344:Tamfang
334:Tamfang
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