Talk:Grand antiprism

Possible net of the anti-prism

It occurred to me that since the grand antiprism divides the 3-spere in two, in the sense of a Clifford torus, you should be able to "unroll" it into a flat square (or perhaps a parallelogram) net of 300 tetrahedra, ten edges on a side, with 100 exposed triangular faces on the top, 100 on the bottom, and 100 internal tetrahedral with only their edges exposed. Cloudswrest (talk) 03:12, 4 September 2013 (UTC)

It further occurred to me that since the 600-cell discrete Hopf fibrates into 20 Boerdijk–Coxeter helices, and since the grand antiprism is just the 600-cell with two sets of 5 Boerdijk–Coxeter helices removed, the grand antiprism is decomposable into a net of 10 Boerdijk–Coxeter helices (and the pentagonal tubes).

In the Hopf fibration mapping from S3 to S2 of the 600-cell to the icosahedron, the subset mapping representing the grand antiprism is an irregular discrete Hopf fibration mapping to the middle row of 10 triangles and the pentagonal faces of the pentagonal antiprism. Cloudswrest (talk) 17:00, 29 September 2013 (UTC)

Schläfli symbol

The page lists the "extended Schläfli symbol" as s{5}.s{5}. That seems to be nonsense. It's of course not a proper Schläfli symbol (those work only for regular polytopes), nor is it an extended Schläfli symbol. --Goomba1729 (talk) 16:57, 10 November 2021 (UTC)

Incorrect description of symmetry group of grand antiprism

The labelling of the symmetry group as the "Ionic diminished Coxeter group $[[10,2+,10]]$" is incorrect, or at best misleading. The actual group does have order 400 but is instead $\pm [D_{10}\times D_{10}]\cdot 2$ in the notation of J. H. Conway and D.~A. Smith , On Quaternions and Octonions, A K Peters, Natick, Mass., 2003, Table 4.3 in Section 4.4. Here $D_{10}$ is the dihedral group of order 10.

The error can be traced back to Section 2.8 of Coxeter's 1985 paper (the first item in the References for the Wikipedia article). That article refers to the group as $[[10,2^{+},10]]\simeq G^{4,4,10}$. The second description $G^{4,4,10}$ is definitely wrong, so the first description $[[10,2^{+},10]]$ is also incorrect, if it is interpreted in the usual fashion. An alternate description of the group given in Koca et al (reference 5 in the Wikipedia article) is basically correct, but does also promote the mislabelling $[[10,2^{+},10]]$.

All this is explained in great detail in my recent article (open access): The Symmetry Group of the Grand Antiprism, Barry Monson, Symmetry 2024, 16(8), 1071; https://doi.org/10.3390/sym16081071

However, since this is original, if minor, research, it seems inappropriate for me to directly edit the article. I need advice. 142.134.84.56 (talk) 17:20, 29 December 2024 (UTC)

Addendum: please excuse the messy fonts and LaTeX symbols. This is my first attempt at editing Wikipedia. Sygpolly (talk) 17:23, 29 December 2024 (UTC)

I hope this helps. —Tamfang (talk) 02:05, 30 December 2024 (UTC)