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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
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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
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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
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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
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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. --
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this is; the reason is because if one takes two cubes of the same size, slices one into six congruent pyramids meeting at its centre, and sticks those onto the faces of the other cube, the result is a rhombic dodecahedron. I think I read that in
690:
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
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article on this basis, but, since the article is already linked in the main content, it should not be linked again in the "See also" section. Does anybody feel the need for me to hand the relevant policy/guideline to them on a plate? — Cheers,
1008:
Ever since the stupid Dec. 2019 encryption protocol upgrade, I can only view or edit
Knowledge 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...
507:
At least the way they display on my monitor, the "A" image has much too heavy and too dark shadows, which obscure some of the structures, while the "B" image has a bunch of similar pastel colors which kind of blend in to each other...
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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.
483:
Image B actually looks more garish due to the huge contrast between light and dark. At the same time, it looks more drab than Image A due to the dull metallic colors. It feels you can reach out and grab Image B.
611:
by Cundy and
Rollett, years ago; maybe a citation should be found and this info incorporated into the article. Incidentally, is there a list anywhere of polyhedra which have this property of tiling 3D space? --
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The darker has deep shadows where faces appear to blend, the brighter has highlights where faces blend. Looking closely, I think that some GIMP-ing could improve the darker image but not the lighter. -- Cheers,
140:
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The chain of logic could be made more explicit! What's obvious is that the acute angle is 2 tan(1/√2) ... I'm not quite awake enough just now to do the derivation from that to cos(1/3). —
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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:
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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.
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The article states "The rhombic dodecahedron can be used to tessellate three-dimensional space. It can be stacked to fill a space much like hexagons fill a plane." But it doesn't say
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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.
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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?). —
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mathematical luminaries. It also prompted an examination of the largely unexplored topic of analogous no-convex polyhedra, which led to unexpected connections and problems."
543:
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.
775:. I am not aware of any significant parallel between the two. For example the rhombic dodecahedron is a quasiregular dual while your average hexagon is not. — Cheers,
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In other words: there are several ways to demonstrate that the RD tiles space, and I wouldn't pick on any one of them as
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This is an article about geometry, not topology, so since it is a different geometry it should be a different article. —
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I agree it should be added, probably here since the topology looks the same. It's mentioned here with a red link
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The double revert confused me. I agree there's no clear connection to a hexagon, although differently, the
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The
Bilinski dodecahedron, and assorted parallelohedra, zonohedra, monohedra, isozonohedra and otherhedra
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is because rhombic dodecahedra are what you get if you squish the spheres of face-centred cubic packing.
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3): face configurations V3.2n.3.2n. I removed the 3-color statement, think that's only true for even
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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The JPEG compression artifacts are really ugly in the original; otherwise it’s a good image.
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Only two? Seems to me there's an infinite sequence of hyperbolic tilings in that family. —
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I think the neighboring face colors fail to be clearly distinguished in the new image.
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have the same relation as a rhombus and hexagon as an elongated rhombus.
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The article could say something more explicit about close-packing. —
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Fair enough if it was just near-simultaneous reverts. — Cheers,
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Consider a hyperbolic triangle whose vertices all have angle π/
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angles on each face measure cos(1/3), or approximately 70.53°.
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reason. But yeah, the cube dissection is worth mentioning. —
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is because all the dihedral angles are 2π/3. No, the reason
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This is an infinite sequence (hyperbolic for all n: -->
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can be the symbolic significance that it "carries".
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times the length of the short diagonal, so that the
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Honeycomb_(geometry)#Space-filling_polyhedra.5B2.5D
985:Why did you alter my sig? Was it a robotic action?
229:This article has not yet received a rating on the
789:Furthermore, a "See also" link was added to the
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941:Architectural meaning and cultural freight
570:The long diagonal of each face is exactly
384:A vote for which honeycomb image is better
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861:A new Rhombic Dodecahedron from Croatia!
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278:cells as well - same packing density.
1053:Unknown-importance Polyhedra articles
893:just added the nice video there too.
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181:This article is within the scope of
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423:Rhombic dodecahedral honeycomb
410:Rhombic dodecahedral honeycomb
212:Template:WikiProject Polyhedra
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757:06:08, 11 December 2020 (UTC)
533:12:45, 22 November 2009 (UTC)
518:17:40, 21 November 2009 (UTC)
498:23:45, 12 November 2016 (UTC)
479:16:40, 21 November 2009 (UTC)
460:19:04, 23 November 2009 (UTC)
446:08:06, 21 November 2009 (UTC)
203:and see a list of open tasks.
109:and see a list of open tasks.
838:21:02, 6 February 2015 (UTC)
804:19:46, 6 February 2015 (UTC)
785:19:43, 6 February 2015 (UTC)
727:02:26, 21 October 2012 (UTC)
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248:The shape of squashed peas
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863:, a standupmaths video.
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924:Wow! Guys -- Thanks.
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846:Bilinski dodecahedron
686:24-cell is an analog?
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773:rhombic dodecahedron
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891:User:David Eppstein
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450:And it's garish. —
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34:content assessment
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253:cool. —
139:on the
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