Talk:Trapezohedron

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Polyhedra

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Pentagonal[edit]

_ _ The graphic is labelled "Pentagonal trapezohedron" (perhaps chosen bcz Dice#Standard variations calls for mention, and a graphic, of that.
_ _ I don't really care whether the term is a mistake or just esoteric; in one case it needs correction but in the other it still needs explanation.
_ _ Describing it with "pentagonal" is radically counter-intuitive, bcz the word means having 5 angles (loosely, corners). This figure has no faces of that kind. Now, the plane vertices of a pentagon are not the kind of things found at the vertices of a solid figure, but even if they are "like" them, it has not 5 vertices but 12, and even if the end vertices are segregated from them, those around the "equator" are not 5 but twice 5. They don't lie in a plane, and the path connecting the ten is not a plane figure. The only pentagons i can associate with the solid figure are cross-sections, perpendicular to the long axis, sufficiently far from the equator.
_ _ The fact that "pentagonal" is a lousy part of any name for this doesn't keep that from being the right name, but if it is the correct name, its weirdness should be acknowledged -- as the absence of trapezoids is.
--Jerzy·t 07:20, 2005 August 11 (UTC)

Visualization[edit]

Some language that may be more appropriate to Trapezohedron has been moved from Dice to Talk:Dice; it may be helpful in the process of fleshing out the stub.
--Jerzy·t 07:20, 2005 August 11 (UTC)

Naming and sides[edit]

I changed name of image from 5-sided trapezohedron (BACK) to "pentagonal trapezohedron". (x-sided means nothing clear at all in this case!)

Top google-search finds a Mathworld definition which looks to be the basis of some of this article content.

http://mathworld.wolfram.com/Trapezohedron.html

There's pages on specific two forms:

http://mathworld.wolfram.com/TetragonalTrapezohedron.html

http://mathworld.wolfram.com/PentagonalTrapezohedron.html

The "pentagonal" part of the name refers to the dual pentagonal antiprism which really has two pentagons in it as faces.

OTHER CONFLICING definition here:

http://www.bartleby.com/61/75/T0327500.html (Any of several forms of crystal with trapeziums as faces.
http://www.elook.org/dictionary/trapezohedron.html [noun] a polyhedron whose faces are trapeziums.

Tom Ruen 07:15, 22 December 2005 (UTC)[reply]

Questioning "Crystal arrangements of atoms can repeat in space with trapezohedral cells."[edit]

If, as I believe, this statement is intended to mean that that the Wigner-Seitz cell of some crystal lattices is shaped like a trapezohedron, then that would imply that 3D-space can be filled without any gaps by stacking repetitions of this trapezohedron. I believe that the only trapezohedron for which this is true is the Triangular Trapezohedron which happens to be a Cube, and that only because the Cube has additional symmetry properties that other trapezohedra do not have. As such, I think the statement is misleading. Just to confuse the issue, some crystals do form a trapezohedral habit: (Search this page for "Trapezohedron") But the habit is only the external shape of the crystal, determined by lowest surface energy; it is not the repeating "cell" out of which the crystal is made. To further confuse the issue, in mineral texts the name "trapezohedron" is often used to refer to the deltoidal icositetrahedron: (A photo of the mineral anaclime)Pciszek 23:30, 7 March 2007 (UTC)[reply]

Trapezoid/trapezium[edit]

The article uses the US forms of trapezoid (two sides parallel) and trapezium (no sides parallel) - in Commonwealth English this is reversed. Checking Trapezium and Trapezoid I can see that Wikipedia prefers the non-US forms. --81.78.159.153 (talk) 18:25, 23 March 2008 (UTC)[reply]

Missing Star Trapezohedra?[edit]

If 7/3 is different than 7/4 then shouldn't 7/5 be different than 7/2 and thus be in the list? Similarly for 9/7, 10/7, 11/8 and 11/9.Naraht (talk) 14:35, 27 February 2015 (UTC)[reply]

@Naraht: They do not exist as uniform duals, because the vertex figure of a uniform n-antiprism would have to violate the triangle inequality for n < 3/2 (this is pretty easy to see, perhaps with a drawing or two). Nonetheless they can exist if you permit the triangles of the dual antiprism to no longer be equilateral. Double sharp (talk) 04:58, 18 November 2017 (UTC)[reply]

Apparently those exist, but not as dual uniforms, but there's no clear reason to limit trapezohedra in this way? Tom Ruen (talk) 05:09, 18 November 2017 (UTC)[reply]

Yeah, I would think that they deserve a showing, although of course with a disclaimer that they are not realisable as dual uniforms. It would also be nice to show the dual antiprisms, presumably at the antiprism article. Double sharp (talk) 12:49, 18 November 2017 (UTC)[reply]

External links to long webpages[edit]

In the Name section, i added a web link, & will add some more, to the very long Crystallography article of the 1911 Encyclopædia Britannica (on Wikisource);

so, just after the "call-to-note" superscript number, between other superscript marks, i specified to go to the figure 27 of this article (far from the beginning).

Is there a better way to add specifications to a "call-to-note" superscript number, please?

@MarkH21: might have an idea on this code issue. ;-)

In advance, thank you very much for your answer!

RavBol (talk) 21:27, 5 April 2021 (UTC)[reply]

@David Eppstein: sorry to bother you again; do you have an idea on this code issue, please?

In advance, thank you very much for your answer!

RavBol (talk) 20:13, 13 April 2021 (UTC)[reply]

Attached superscript annotations to superscript footnote markers, as you added here and as the {{rp}} template adds more generally, are an abomination. Just make a new footnote <ref>Encyclopædia Britannica, Fig. 27</ref> or whatever. —David Eppstein (talk) 22:50, 14 April 2021 (UTC)[reply]