Talk:Rhombic dodecahedron

message: If you get a bunch of malleable spherical objects and apply uniform pressure to them, for instance if you squeeze a bag of peas, the objects approximate rhombic dodecahedra. I hesitate to add this to the article, because I have no source and it's a fairly vauge statement anyway, but I think it's cool. —Keenan Pepper 04:35, 22 April 2006 (UTC)
replies: text: The article could say something more explicit about close-packing.  —Tamfang 05:34, 22 April 2006 (UTC)

text: You can also get Trapezo-rhombic dodecahedron cells as well - same packing density. Tom Ruen 06:54, 22 April 2006 (UTC)
thread_title:  The shape of squashed peas 

message: Only two?  Seems to me there's an infinite sequence of hyperbolic tilings in that family. —Tamfang (talk) 09:44, 16 July 2008 (UTC)
replies: text: This is an infinite sequence (hyperbolic for all n>3): face configurations V3.2n.3.2n. I removed the 3-color statement, think that's only true for even n. Tom Ruen (talk) 21:27, 16 July 2008 (UTC)
replies: text:  Consider a hyperbolic triangle whose vertices all have angle π/n; 'kis' it, so that it has three pieces in three colors.  If the sides of the original triangle are mirrors, you have the desired three-coloring of H2, whether n is even or odd. —Tamfang (talk) 04:26, 10 August 2008 (UTC)
thread_title:  Related polytopes 

message: : The rhombic dodecahedron is 1 of the 9 edge-transitive convex polyhedra, the others being the 5 Platonic solids, the cuboctahedron, the icosidodecahedron and the rhombic triacontahedron.
Here and elsewhere, number-words were recently replaced with numerals.  In some contexts, like the number of faces, I don't care one way or the other; but it feels wrong to me (unless words would be awkward) to use numerals rather than words for the size of a set when that size can only be found by direct enumeration.  (Does that make sense?)  To use a numeral for the trivial one-ness of a single entity – "is 1 of" – smacks of preciosity (or is that only a French word?). —Tamfang (talk) 02:45, 5 March 2009 (UTC)
thread_title:  numerals or words 

message: A<BR>Original	B<BR>Brightened
             	
Image A:
# I think the neighboring face colors fail to be clearly distinguished in the new image. Tom Ruen (talk) 08:06, 21 November 2009 (UTC)
thread_title:  A vote for which honeycomb image is better 

message: The rhombic dodecahedron can also be constructed by packing together four like solids, rhombic hexahedra, which have six rhombic faces and resemble semi-squashed cubes.
Space filled entirely by rhombic dodecahedra may be sliced by a plane in one orientation to reveal a pattern of hexagons, and in another orientation to reveal a pattern of squares.
173.166.70.197 (talk) 19:13, 17 September 2010 (UTC)
thread_title:  Rhombic hexahedra and other interesting properties of the rhombic dodecahedron 

message: : The long diagonal of each face is exactly √2 times the length of the short diagonal, so that the acute angles on each face measure cos−1(1/3), or approximately 70.53°.
The chain of logic could be made more explicit!
What's obvious is that the acute angle is 2 tan-1(1/√2) ... I'm not quite awake enough just now to do the derivation from that to cos−1(1/3). —Tamfang (talk) 18:08, 26 April 2011 (UTC)
thread_title:  face angles 

message: At the bottom of this article there is a link to the 24-cell, and it says that the 24-cell is the 4 dimensional analog of the rhombic dodecahedron. I don't know what the 24-cell and the rhombic dodecahedron have in common at all. Please explain Tntarrh (talk) 01:30, 21 October 2012 (UTC)
replies: text: Each is dual to a rectified cross-polytope. --Tamfang (talk) 02:26, 21 October 2012 (UTC)

text: The Rhombic dodecahedron and the Cuboctahedron as a pair capture different aspects of the features of the 24-cell in 3 dimensions.  The rhombic dodecahedron has identical faces with equal edge lengths, but fails to be regular because not all angles in a rhombus are the same.  In contrast the cuboctahedron has all equilateral faces, but they are a mix of squares and equilateral triangles.  Both of these are possible 3D cross sections of the 4D 24-cell.  All of the other regular 4D polytopes have a single regular 3D analog, so the 24 cell is unique in mapping only partially onto two rough 3D analogs.  -- JasonHise (talk) 06:08, 11 December 2020 (UTC)
thread_title:  24-cell is an analog? 

message: : The Rhombic dodecahedron and the Cuboctahedron as a pair capture different aspects of the features of the 24-cell in 3 dimensions.  The rhombic dodecahedron has identical faces with equal edge lengths, but fails to be regular because not all angles in a rhombus are the same.  In contrast the cuboctahedron has all equilateral faces, but they are a mix of squares and equilateral triangles.  Both of these are possible 3D cross sections of the 4D 24-cell.  All of the other regular 4D polytopes have a single regular 3D analog, so the 24 cell is unique in mapping only partially onto two rough 3D analogs.  -- JasonHise (talk) 06:08, 11 December 2020 (UTC)
thread_title: 2020

message: Hello All - someone more math-aware than me should please add to this article about the Bilinksi dodecahedron, discovered in 1960, which is of a different form.  Here are two web links:
* The Bilinski dodecahedron, and assorted parallelohedra, zonohedra, monohedra, isozonohedra and otherhedra, a pdf file
* A new Rhombic Dodecahedron from Croatia!, a standupmaths video.
From the abstract: "Fifty years ago Stanko Bilinski showed that Fedorov's enumeration of convex polyhedra having congruent rhombi as faces is incomplete, although it had been accepted as valid for the previous 75 years. The dodecahedron he discovered will be used here to document errors by several mathematical luminaries. It also prompted an examination of the largely unexplored topic of analogous no-convex polyhedra, which led to unexpected connections and problems."  user:JMOprof ©¿©¬ 14:29, 27 May 2016 (UTC)
replies: text: I agree it should be added, probably here since the topology looks the same. It's mentioned here with a red link Stanko Bilinski, and it looks like User:David Eppstein just added the nice video there too. Tom Ruen (talk) 15:58, 27 May 2016 (UTC)
replies: text: This is an article about geometry, not topology, so since it is a different geometry it should be a different article. —David Eppstein (talk) 17:42, 27 May 2016 (UTC)
thread_title:  Bilinski dodecahedron 

message: Can you make sense of this new section?  If it is as meaningless as I suspect, the same matter needs removing from several other articles.  I'll mention in passing that its author has been banned for sockpuppetry. --Tamfang (talk) 02:33, 4 May 2024 (UTC)
replies: text: "Freight" should be "Weight", but I still don't know what it's supposed to mean... AnonMoos (talk) 05:10, 4 May 2024 (UTC)
replies: text: Well, freight can be the symbolic significance that it "carries".  --Tamfang (talk) 22:25, 4 May 2024 (UTC)
replies: text: Ever since the stupid Dec. 2019 encryption protocol upgrade, I can only view or edit Wikipedia from home in a somewhat roundabout way using a non-fully-Unicode-compliant tool.  I can point you to some previous boring discussions about this... AnonMoos (talk) 00:15, 5 May 2024 (UTC)
thread_title:  Architectural meaning and cultural freight