Talk:Elongated dodecahedron
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Removed statement just added: Unclear what the "symmeties" are, and not a very useful die with unequal face areas. Tom Ruen 01:47, 30 November 2006 (UTC)
- It has 12 faces,over 120 symetries,and can be used as a 12 sided dice in board games.
I added that it has D4h symmetry, which looks like order 16 symmetries. Tom Ruen 02:17, 30 November 2006 (UTC)
Wigner-Seitz cell for a body-centered cubic lattice?
editI a almost certain that a rhombic dodecahedron is the Wigner-Seitz cell for a *face centered* cubic lattice. Every lattice point in a FCC lattice has 12 nearest neighbors, so the Wigner-Seitz cell should have 12 faces. Every point in a BCC lattice has eight nearest neighbors and six second-nearest neighbors, and the Wigner-Seitz construction produces a truncated octahedron. Maybe the original author was thinking of Brillouin zones, which are Wigner-Seitz cells in reciprocal space. --Pciszek 04:08, 4 January 2007 (UTC)
- I create the stub but I can't judge that addition. Tom Ruen 04:54, 4 January 2007 (UTC)
- @Pciszek: An old discussion, but your logic is correct for rhombic dodecahedron. However, this is the page for the elongated dodecahedron, not the ordinary dodecahedron. Because it's elongated, it's the Wigner-Seitz cell of the body-centered tetragonal lattice, not body-centered cubic lattice. Body-centered cubic and face-centered cubic are different lattices, but the face-centred tetragonal lattice is identical to the body-centered tetragonal lattice, so the article is actually correct. 〈 Forbes72 | Talk 〉 02:09, 6 October 2020 (UTC)
Inaccurate drawing
editThe drawings of this shape here are inaccurate: the four hexagon-hexagon edges are drawn shorter than the other edges. One might argue that it's something to do with perspective, but no: in the perspective shown, these edges should if anything appear slightly longer than the other edges, because they're perpendicular to the direction of projection and the others aren't. Any chance of a fix? —David Eppstein (talk) 02:19, 13 August 2010 (UTC)