Talk:Trapezohedron

message: 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)
thread_title:  Naming and sides 

message: 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)
thread_title:  Questioning "Crystal arrangements of atoms can repeat in space with trapezohedral cells." 

message: 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)
thread_title:  Trapezoid/trapezium 

message: 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)
replies: text: 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)

text: 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)
replies: text: 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)
thread_title:  Missing Star Trapezohedra?