Talk:Trapezohedron
Pentagonal
_ _ 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
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
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.
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)
Questioning "Crystal arrangements of atoms can repeat in space with trapezohedral cells."
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)