Talk:Honeycomb (geometry)

message: Shouldn't this be merged into Tessellation? --PeR 19:23, 28 March 2006 (UTC)
thread_title: Merge

message: Congruency of vertices is insufficient, as the pseudorhombicuboctahedron (J37) illustrates for finite polytopes.  Consider an elongated triangular prismatic tiling in which one layer of cubes is bisected and rotated, so that on one side of the cut-plane (call it the XY plane) the axis of the 3-prisms is parallel to the X axis, on the other side they are parallel to the Y axis.  The symmetry group then has no Z component and therefore vertices at different Z are in different equivalence classes; this tiling is not uniform although each vertex figure is the same.  —Tamfang 01:08, 11 June 2006 (UTC)
thread_title:  definition of uniform 

message: I have created a new sub-:Category:Honeycombs (geometry) page and re-categorised some of the individual honeycomb pages. Anybody feel like helping with the rest? To find them, browse to :Category:Polytopes or :Category:Tiling Steelpillow 17:04, 8 March 2007 (UTC)
replies: text: I converted them all I think, changed to lower case (geometry). Tom Ruen 22:41, 8 March 2007 (UTC)
thread_title:  Category:Honeycombs (geometry) 

message: The first two sentences read:
"In geometry, a honeycomb is a space filling or close packing of polyhedral cells, so that there are no gaps. It is a three-dimensional example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycomb is also sometimes used for higher dimensional tessellations as well. For clarity, George Olshevsky advocates limiting the term honeycomb to 3-space tessellations and expanding a systematic terminology for higher dimensions: tetracomb as tessellations of 4-space, and pentacomb as tessellations of 5-space, and so on."
But Coxeter, who I believe invented the term, used it consistently for a tessellation of not only 3-dimensional space, but for any dimension.  
With much due respect for George Olshevsky: I believe Coxeter's usage carries vastly greater weight, and that it is vastly inappropriate for an article to be based on what "George Olshevsky advocates", regardless of how nice his polytope website is.
(One reason: Searching on MathSciNet for all papers authored by H.S.M. Coxeter gives 254  results; searching for all papers authored by George Olshevsky; or Olshevsky, George; or G. Olshevsky; or Olshevsky, G. yields 0 results.)
This strongly suggests this article should be merged with that of Tessellation.Daqu (talk) 00:35, 29 August 2008 (UTC)
replies: text: I agree that the title and content are a poor match. Although Olskevsky is at the forefront of current activity in polytope discovery and enumeration, he seldom publishes his results formally. He is also fond of coining his own jargon. So overall I think you are right about Coxeter vs. Olshevsky too. Also, the geometric tilings/tessellations/honeycombs articles are all in a mess. Not, of course, helped by the fact that all three terms are mostly interchangeable. But I think merging this article with Tessellation would be wrong, because this focuses on 3D while the other focuses on 2D. No doubt somewhere these are articles on 4D too. Also, very likely, there are articles which muddle tilings generally with regular and uniform varieties. IMHO we need a single "home" article (I would suggest Tiling (geometry) as the plainest and clearest) giving an overall summary, with Tessellation and Honeycomb (geometry) as redirects, and build up a set of sub-topics from there. Meanwhile, some pruning of the "Olshevsky advocates" stuff would be welcome. -- Cheers, Steelpillow (Talk) 08:49, 29 August 2008 (UTC)
thread_title: Why does someone think a honeycomb is only 3-dimensional???

message: Norman Johnson has some terminology, but all seems to apply specifically to face-to-face honeycombs. Tom Ruen (talk) 05:30, 4 May 2017 (UTC)
thread_title:  Some ''n''-dimensional terminology