Talk:Grand antiprism
Latest comment: 3 years ago by Goomba1729 in topic Schläfli symbol
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Possible net of the anti-prism
editIt 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
editThe 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)