Talk:Bipyramid

Architecture of a bipyramid

An architecture of a complex pyramids

Complex of the pyramids constructed of glass, metal, stone, ceramics, tree, amber and other materials

The information on architecture and details of a complex pyramids has been received by means of a framework dowsing and channelling. In work materials results of researches in the field of alternative medicine where it is revealed are in more details stated, that the architecture of pyramids can is applied in the medical purposes. In this work it is shown, how the physical form of a matter influences movement of the radio form of a matter (the Spirit substance). And all it is carried out by means of architecture of making components of a pyramid. In work photos of development of architecture of a complex of pyramids are presented[1].

Bipyramid (Magic Staff)

Magic staff (Bipyramid)

The basic materials of which the staff is made: aluminium, copper, iron, zinc, a brass, cupronickel, quartz, glass, lazurite, a nephrite, a jasper, corals, turquoise, amber, a cedar. —Preceding unsigned comment added by Shatilov Konstantin (talk • contribs) 18:08, 26 December 2007 (UTC)

Architecture of a bipyramid in the Temples

[[2]] —Preceding unsigned comment added by 91.122.151.50 (talk) 10:49, 26 December 2007 (UTC)

--Shatilov Konstantin 12:10, 14 September 2007 (UTC)

What are these called? Skew bipyramids?

Take a bipyramid, cut it in two along its equator, and rotate one of the halves so that its vertices alternate, around the equator, with the vertices of the other half. Take the convex hull of the result. It has kite-shaped faces, and is face-transitive. What is it called? I think it is regular enough to deserve an article. Or maybe it has an article already, which should be linked to from this one. Maproom (talk) 12:20, 15 October 2012 (UTC)

If the original is an n-bipyramid, seems to me you have a 2n-bipyramid. —Tamfang (talk) 19:13, 15 October 2012 (UTC)

Yes, of course you do. Stupid of me. What I should have said is, as well as rotating one half, separate the two halves by exactly enough that the faces of the convex hull are four-sided, kites in fact. (For the special case of the triangular bipyramid, the kites are squares, and the result is a cube.) Maproom (talk) 19:31, 15 October 2012 (UTC)

It's the dual of an antiprism and it is called ... (clickety click) ... a trapezohedron, among other names. —Tamfang (talk) 19:56, 15 October 2012 (UTC)

Thank you! Maproom (talk) 22:28, 15 October 2012 (UTC)

Partial writing

@Jacobolus. Sorry, I did not see you have edit the article in the last day. I have removed the sections, merging into one section that includes the equilateral, and symmetry. The rest of the section that I have planned is trying to merge into one sections, since most of them are talking about the "other types and related polyhedra". Dedhert.Jr (talk) 05:08, 24 January 2024 (UTC)

Are you still adding stuff back then? I think the previous tables were too big before, but somewhat useful: it's worth talking about the symmetries of 3-space / the sphere, etc. I think the infobox also seemed valuable (but I shrank the images inside a bit). –jacobolus (t) 06:30, 24 January 2024 (UTC)

To be specific, I think this table is more useful than this set of images:

Regular right symmetric n-gonal bipyramids:

Bipyramid name	Digonal bipyramid	Triangular bipyramid	Square bipyramid	Pentagonal bipyramid	Hexagonal bipyramid	...	Apeirogonal bipyramid
Polyhedron image						...
Spherical tiling image						Plane tiling image
Face config.	V2.4.4	V3.4.4	V4.4.4	V5.4.4	V6.4.4	...	V∞.4.4
Coxeter diagram						...

The triangular bipyramid, octahedron, and pentagonal bipyramid.

–jacobolus (t) 06:36, 24 January 2024 (UTC)

@Jacobolus I prefer to say that the table contains the images, spherical tiling, face configuration, and Coxeter diagram are not essentially useful, as the article mentions bipyramid only, and its types and related polyhedra. The reason that I use the images is that the first paragraph mentions the example of regular bipyramids. All of those three in those cells may be exhibited specifically in each article. Also, do you have some sources for regular and right bipyramid terminologically? It may be helpful to expand the first section of "Description". Dedhert.Jr (talk) 02:37, 25 January 2024 (UTC)

Sources can certainly be found for this, but it might take some searching. These terms are all inherited from the terminology for pyramids. It might be useful to consolidate discussion of "irregular", asymmetric, oblique, etc. bipyramids into one top-level section, though I'm not sure what heading that would have.

I think this article should also discuss "bipyramidal symmetries", including as point groups, spherical tilings, etc., and including those rows in the table seems very helpful for that. –jacobolus (t) 04:16, 25 January 2024 (UTC)

Interestingly, Polya has a slightly different definition of right pyramid / "right double pyramid" than Mathworld, though they agree when the base is a regular polygon. For Polya, a right pyramid must have its apex on the line perpendicular to the base through the incenter, and the base must be a tangential polygon, whereas for Mathworld a right pyramid must have its apex on the line perpendicular to the base through the centroid. Mathematics and Plausible Reasoning p. 138 https://books.google.com/books?id=-TWTcSa19jkC&pg=PA138. –jacobolus (t) 04:38, 25 January 2024 (UTC)

@Jacobolus What an interesting name. I will added them. For the spherical tillings, I have no idea whether they are helpful or not. As our article Spherical polyhedron or spherical tilling states, "a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons". As a mathematics-lover-but-have-no-knowledge-instead-learning-from-the-sources user, the section should provide more explanation, although some of its tables describes the spherical polyhedron for three symmetries. Dedhert.Jr (talk) 08:05, 25 January 2024 (UTC)

Here's a source with some historical discussion about the name: http://www.minsocam.org/ammin/AM20/AM20_838.pdf –jacobolus (t) 02:35, 26 January 2024 (UTC)

One reason I think the table is helpful is that it shows the general pattern. It's valuable to make it explicit that this can be described systematically; the isolated example images take away context and make it harder for readers to make sense of. In other parts of this article I think we can cut some of the over-abundant examples, but a table where we just do the first few cases and then a ... doesn't seem excessive. –jacobolus (t) 07:57, 26 January 2024 (UTC)

@Jacobolus It's fine if you want to keep the tables, but we need to modify them a little bit. For example, does the spherical tillings and Coxeter diagrams actually help readers to comprehend these somewhat technical? I do think that some of them would never understand those notations, as the content of our article Coxeter diagram have some problematic things. Dedhert.Jr (talk) 11:48, 26 January 2024 (UTC)

I think the spherical tilings are helpful, but they should be explained in the text. –jacobolus (t) 15:52, 26 January 2024 (UTC)

I don't feel like I understand Coxeter diagrams well enough to rewrite that article, but the mass of banners at the top seems pretty excessive. Perhaps someone at WT:WPM could be talked into writing a clearer basic explanation. –jacobolus (t) 19:55, 26 January 2024 (UTC)

Are there any sources about star bipyramids, etc.?

I am not finding a lot in my attempts at a literature search. So far I can find one source which doesn't really describe/define a star dipyramid, but invokes it to describe some historical artifacts, and only one source doi:10.1016/0097-8493(88)90036-2 which describes it. –jacobolus (t) 06:52, 26 January 2024 (UTC)

@Jacobolus Ahh... sorry for interrupting. But I couldn't access neither of them, so I could not check the verifiability. Dedhert.Jr (talk) 10:36, 26 January 2024 (UTC)

The latter source doesn't really say much at all. It just gives some code for drawing a "star dipyramid":

star_pyramid(n, a, h) = n(S_0; Y 4π/n; S_1; Y-2π/n) [...]

star_dipyramid(n, a, h) = star_pyramid(n, a, h); star_dipyramid(n, a, -h).

Earlier it explains what it means by this notation. –jacobolus (t) 15:06, 26 January 2024 (UTC)