Talk:Tetrahedron

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Polyhedra

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( Written before TOC )

Maybe I'm just spacially challenged, but I can't agree with the following sentence from the article:

A tetrahedron can be embedded inside a cube so that each vertex is a vertex of the cube, and each edge is a diagonal of one of the cube's faces.

If you obey "each vertex is a vertex of the cube", then the statement that "each edge is a diagonal of one of the cube's faces" is wrong, maximally three edges of the tetrahedron can be diagonals of the cube, the others must lie on the edges of the cube. WDYT? --snoyes 00:17 Feb 26, 2003 (UTC)

Consider vertices at (0, 0, 1), (0, 1, 0), (1, 0, 0) and (1, 1, 1) on the unit cube.

The edges of the tetrahedron made by these points are:

(0, 0, 1), (0, 1, 0)
(0, 1, 0), (1, 0, 0)
(0, 0, 1), (1, 0, 0)
(0, 0, 1), (1, 1, 1)
(0, 1, 0), (1, 1, 1)
(1, 0, 0), (1, 1, 1)

All face diagonals (I think: it's late, I'm tired). The Anome 00:35 Feb 26, 2003 (UTC)

Yip, I'm just spaTially (and spelling) impaired. Thanks for your time. --snoyes 01:24 Feb 26, 2003 (UTC)

The buckminster-fuller web site has a great animation that shows this :-) -- Tarquin 11:11 Feb 26, 2003 (UTC) ... and I can't find it on Google. I have it on my HD though, email me Snoyes and I'll send it back to you :-)

A cube can be divided into five tetrahedra. The central one is a regular tetrahedron whose edges are the diagonals of the cube's faces. The other four tetrahedra are not regular with three edges diagonals of the cube and the other threee edges edges of the cube. Thus everything said above is correct. You're just talking about different tetrahedra.

Edges of a tetrahedron

How many edjes does it have 212.129.77.225 (talk) 19:38, 9 February 2022 (UTC)[reply]

Six. 2A00:23C7:548F:C01:74DF:CE53:6F62:D4DC (talk) 18:55, 7 February 2023 (UTC)[reply]

Application: Packaging

The now-rare tetrahedral Tetra Pak Classic carton shipped in hexagonal crates, and is the origin of the packaging multinational's name. There are supporting photos in the article about the company, including:

scruss (talk) 16:23, 19 July 2022 (UTC)[reply]

@Scruss. This is interesting. Sorry for the three-years-delayed-reply. I wonder there is a source to provide this. Dedhert.Jr (talk) 02:58, 24 July 2025 (UTC)[reply]

That image is originally from Tetra Pak's own Flickr stream: Tetra Pak® - Housewife at the dairy counter in a Swedish shop. Image from the 1950's. For reference HI10262. But there's a much clearer example here: Tetra Pak® - Tetra Classic® Aseptic packages in steel baskets, 1960s. Tetra Pak. For reference: HI10178. Both are under an old CC licence, so care may be needed with reusing them — scruss (talk) 18:05, 26 July 2025 (UTC)[reply]

@Scruss. I meant the reliable sources, like website of news, books, and journals. Dedhert.Jr (talk) 14:47, 28 July 2025 (UTC)[reply]

I'd forgotten about the irritating source rules here. Anyway, how about:

14 april 1954: Mjölk i Tetra Pak lanseras - Bizstories - which has the requisite pictures and is from some kind of news agency;
US 2742181A Containers that can be telescopically inserted into each other and at the same time be stacked upon one another and USD168842S: Combined tetrahedronal shaped packages and container therefor - Harry Järund's patents for the packaging and crates.

scruss (talk) 22:21, 28 July 2025 (UTC)[reply]

multiple tetrahedral family that can be folded on a single A4 sheet

2^N multiple tetrahedral family that can be folded on a single rectangle sheet

Using a sheet of √1:√2 paper such as A4, you can fold a tetrahedron with four identical √3:√4 isosceles triangular faces into multiple pieces that are multiples of 2^N without cutting. Each of these tetrahedrons has four triangular paper faces, which do not overlap. That is, there are four times as many triangular faces as there are tetrahedra. In the case of a single sheet, groups of 2, 4, 8, and 16 tetrahedra of the same size are folded in various strange ways. Also, if you follow a certain rule (pattern), you can fold an infinite number of 2^N tetrahedra. 183.177.128.238 (talk) 05:20, 29 November 2023 (UTC)[reply]

Thanks, but sorry because we need reliable sources, not the original research. Dedhert.Jr (talk) 03:13, 11 September 2024 (UTC)[reply]

Proposal: split regular tetrahedron to have its own article

I recently pondered that the regular tetrahedron should have its article, just like how regular octahedron is supposed to be. And somehow, the article's main purpose is to describe what a tetrahedron should be in general. So I propose this idea, unless the applications of the regular tetrahedron remain. Dedhert.Jr (talk) 02:01, 22 July 2025 (UTC)[reply]

It looks like there was an article for regular tetrahedron up until about 2021, where a large amount of edit warring took place. I wouldn't be opposed to having a separate article–in fact, I assumed that an article already existed until I saw this. GregariousMadness (talk to me!) 08:54, 22 July 2025 (UTC)[reply]

Clarifying comment to support proposal. GregariousMadness (talk to me!) 01:01, 23 July 2025 (UTC)[reply]

Support There is enough content about special properties of the regular tetrahedron. –LaundryPizza03 (d c̄) 14:53, 22 July 2025 (UTC)[reply]

Support as a notable concept on its own and with substantial material. I also note it's the only Platonic solid without a standalone article. fgnievinski (talk) 18:23, 24 July 2025 (UTC)[reply]

Comment. The edit warring in 2021 was all due to a single long-term abusive editor and sockpuppeteer, Wikipedia:Long-term abuse/Xayahrainie43. It should be disregarded when evaluating the current proposal. —David Eppstein (talk) 18:31, 26 July 2025 (UTC)[reply]