User:Dc.samizdat/Radially golden polychora

Author: David Brooks Christie

Plan
Envision this paper as collecting only my own (in some cases possibly original) observations, as concisely as possible, without the requirement of accessibility - not as an enyclopedic survey of the known properties of any polychora; for those see e.g. the 600-cell article to which I have made contributions.

Definition of radially golden polytopes (original terminology). The central golden apex vertex (terminology)?

Additional hypercubic chords of the 600-cell ($\sqrt{5}$ and its golden ratio subdivisions). Credit Steinbach.

Use of Hopf coordinates to elucidate the 600 5-cells, and the translation between Hopf and Cartesian to facilitate rotations and non-orthogonal relationships generally (not original, credit PAR, and JEMebius for Rotations).

The 600-cell vertex as 3/4-transicosahedron; see also Trans polytopes.

The 5-fold inscribed 4-polytopes in the 600-cell and 120-cell, as isoclinic (or single?) rotations through π/? and π/? respectively.

Visualization of cell boundaries of interior 4-polytopes (of 24-cell, 600-cell and 120-cell) as polychoric rings (Hopf fibrations), their overlaps and interstices (not original, credit Cloudswrest).