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The first paragraph of the section D4 lattice reads as follows:
"Its vertex arrangement is called the D4 lattice or F4 lattice. The vertices of this lattice are the centers of the 3-spheres in the densest possible packing of equal spheres in 4-space; its kissing number is 24, which is also the highest possible in 4-space.'
But I do not believe that anyone has ever determined the densest possible packing of equal spheres in 4-space!
(Maybe D4 represents the densest possible packing of equal spheres among lattice packings. That is usually much easier to determine than the densest sphere packing among all packings whatsoever.)
I hope someone knowledgeable on this subject will correct this, if in fact it needs correction.Daqu (talk) 20:19, 24 August 2016 (UTC)
The article refers to "4-demicubic lattices" and to "5-demicubic honeycombs", but there is no reference to the definition of such things.
The article Alternated hypercubic honeycomb seems to be the only place in Wikipedia where such things are defined, but the definition could hardly be more vague for non-experts:
"In geometry, the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation operation."
Whatever "with an alternation operation" means!
Both that article and this one need to have a clear definition in English or reference to what a "demicubic lattice" and a "demicubic honeycomb" mean!
Sure, the Coxeter diagrams are a useful shorthand, but that's no reason to omit a definition in English.Daqu (talk) 17:38, 20 September 2016 (UTC)
The article titled D4 lattice contains statements about both the D+
4 lattice and the D*
4 lattice.
But there is nothing whatsoever to explain what connection, if any that these two lattices may have with the subject of the article: the 16-cell honeycomb of 4-dimensional space.
To make matters worse, this section also includes this paragraph:
"This packing is only a lattice for even dimensions. The kissing number is 23 = 8, (2n – 1 for n < 8, 240 for n = 8, and 2n(n – 1) for n > 8)."
Since only 4-dimensional lattices have been mentioned, it could hardly be more unclear what "This packing" refers to.
And what kissing number is referred to by "The kissing number" is also utterly unclear.216.161.117.162 (talk) 18:20, 27 September 2020 (UTC)
The first sentence epitomizes bad writing. It reads:
"In four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {3,3,4,3}, and constructed by a 4-dimensional packing of 16-cell facets, three around every face."
Every face??? Are we trying to inform readers or confuse them?
Since we're talking about 4-dimensional geometry, a "face" of a honeycomb is likely to be understood as one of the 3-dimensional components of it, in other words a 16-cell.
Or if the 16-cells are understood as being referred to here, a reader might think that "face" means one of one of their faces: a tetrahedron.
But no: Here the word "face" means a 2-dimensional face. How difficult would it be to just say so?
There is no excuse for such bad writing.2601:200:C000:1A0:6432:8815:CF92:7252 (talk) 01:49, 31 May 2021 (UTC)