Talk:Bilinski dodecahedron

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«These zonohedra are projection envelopes of the hypercubes...»

 * In the Bilinski dodecahedron section, in the § starting with «These zonohedra are projection envelopes of the hypercubes, with n-dimensional projection basis, with golden ratio (φ)...»:
 * I don't know whether «These zonohedra» include the 2 golden rhombohedra (projection envelopes of the cube?) & the golden rhombus (projection envelope of the square?); do you, please?
 * I don't understand how a given point of an n-cube is actually projected onto the corresponding zonohedron with golden rhombic faces; do you, please?
 * In advance, thank you very much for your answers! —JavBol (talk) 00:02, 11 November 2022 (UTC)
 * I am not familiar with the details of the individual projections here. The "Projective n-cube image" at the bottom of the table shows how the various j-faces of the n-cube map onto and into the image zonohedron. One can think of the n-cube's higher dimensions as collapsing into the internal structure of the 3D polyhedron; the outer surface of the zonohedron is formed only by those 0, 1 and 2-faces of the n-cube which happen to project onto that position and are not hidden inside. An example transformation matrix, for n = 6, is offered above the table. I agree that it is all badly explained and the language is ambiguous.
 * Does the term "hypercube" include the point, line segment, square and cube? The article on the Hypercube claims that it does, but does not cite a source for this claim so it could be wrong; I have now added a citation tag there. (One reason I prefer Coxeter's "measure polytope" for the general class). This indeed makes it difficult to say which figures "these zonohedra" is intended to cover.
 * Also, I think this whole section does not belong here, it should be within the main Zonohedron article.
 * As it happens, I have recently updated my own web page on this polyhedral dissection (though in the context of quasicrystals not n-cubes), here. But it is not peer reviewed, so should not be cited here.
 * Hope this helps. &mdash; Cheers, Steelpillow (Talk) 05:40, 11 November 2022 (UTC)
 * Hope this helps. &mdash; Cheers, Steelpillow (Talk) 05:40, 11 November 2022 (UTC)