Talk:600-cell

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Start a topic on this page that is relevant to the 600-cell article but not present in it yet, or that is incompletely or wrongly described. Point out what is missing in the article, question its findings (perhaps some things in the article are wrong), or ask a question about something you don't understand, in the article or about its subject generally.

Your question does not have to be inspired or especially deep for you to ask it by starting a topic on this page. If there is already a topic here that is somehow related to it, it may be best to ask your question as a reply to that topic, but this Discuss page doesn't have to be perfectly organized; it is only important that a conversation develops. Try to answer a question on this page, or make a suggestion about how to approach that question. Participate and contribute.

Simple questions are not stupid, and they are usually helpful, because the people who contributed the text of the article are often the least likely to understand how it fails to describe the subject adequately to someone who isn't already an expert in it. Anyone who provides thoughtful feedback is a participant in this research.

All scientific discovery begins by asking a question, and often the most naive questions turn out to be the most illuminating, and lead to original discoveries. Dc.samizdat (discuss • contribs) 15:39, 19 May 2024 (UTC)

Hopf spherical coordinates

This section introduces the Hopf coordinates and gives the rationale for using them to describe 4-polytopes, and some references, but no further use is made of this kind of coordinates elsewhere in the article. The section gives the Hopf coordinates for the $H_{4}$ polytopes, explaining that these are the coordinates of the whole 600-point 120-cell, but the specific Hopf coordinates of the 120-point 600-cell that is the subject of this article are not identified. Elsewhere throughout the article some use is made of Cartesian coordinates, but Hopf coordinates are not given, and currently they are never mentioned again. Please improve this article by using Hopf coordinates to illustrate features of the 600-cell. Dc.samizdat (discuss • contribs) 16:20, 19 May 2024 (UTC)

Kinematics of the cuboctahedron

Consider the cuboctahedron transformation cycle as a motion in 4 dimensions, as Coxeter did (see citation after "helical contraction"). The pyritohedral symmetry transformation is said to be the only 3D transformation which is neither a reflection nor a rotation. Could it be a 4D Boole Stott expansion, e.g. of the faces of the 24 octahedra of the 24-cell into cuboctahedra or icosahedra in the 600-cell? The expanding octahedron vertices move along helical paths in a Möbius loop, as do vertices of a 4-polytope under isoclinic rotation. Are those expanding octahedron vertex paths related to rotation isoclines, and if so, of which discrete isoclinic rotation, characteristic of which 4-polytope? Dc.samizdat (discuss • contribs) 06:33, 22 October 2024 (UTC) Is every Boole Stott expansion characterizable as an isoclinic rotation? Is there an equivalence between the general operations of dimensional analogy and the isoclinic rotations with their Hopf fibrations? Dc.samizdat (discuss • contribs) 19:49, 25 October 2024 (UTC)

Liskov substitution principle

This semantic subtyping relation is useful for characterizing the relations among polytopes and other invariant objects (such as their rotations), in particular the containment relationships among their properties. It is only one possible subtyping relation, and undecidable in general, but it is strong enough to constrain the behaviors (semantics) and knowability (encapsulation) of the related objects. Dc.samizdat (discuss • contribs) 19:00, 25 October 2024 (UTC)