# Comments on Des figures que j'en ai marre de refaire, et des histoires de kaléidoscopes

## En perspective (2018-09-01T10:51:15Z)

"Ce qu'il faudrait vraiment faire, en revanche, c'est une représentation des trois kaléidoscopes euclidiens en dimension 3 (c'est-à-dire A₃˜, B₃˜ et C₃˜, cf. ci-dessus), un peu comme j'ai fait mes figures en dimension 2, et de façon à permettre aux gens comme moi incapables de voir dans l'espace de s'y retrouver un peu."

Qu'est-ce que tu appelles voir dans l'espace ? Ton cerveau est programmé pour voir en trois dimensions ; même des choses qui sont en deux dimensions on peut les dessiner de manière à ce qu'elles te donnent l'illusion de la troisième dimension.
NB Invention par Brunelleschi de la perspective faute d'arriver à dessiner correctement le Baptistère octogonal de Florence.

## jonas (2018-08-31T00:23:32Z)

> La condition supplémentaire en question peut s'exprimer de différentes manières qui sont, il me semble, équivalentes

But they're only really equivalent if you also tell what kind of underlying spaces you accept, even in two dimensions, otherwise someone could play silly games like claiming that they live on the (unoriented) projective plane with the elliptic metric and cover it with 24 triangles with angles $\\pi/4, \\pi/6, \\pi/8$, which I think satisfies the tiling property and the third phrasing of your extra condition but not the first phrasing. Perhaps I didn't get that example right, but even then there'll probably be some example that breaks the equivalence or some other statement in your post, such as the one starting with “En supposant que le simplexe ayant un certain ensemble d'angles dièdres existe bien, et que ces angles sont tous de la forme π/m pour m entier ≥2,”. And to avoid this without being too restrictive about the underlying spaces, you'd have to explain what you told in the Lie group post <URL: http://www.madore.org/~david/weblog/d.2015-04-24.2292.liegroups.html#d.2015-04-24.2292 > about the π₀ and π₁ phenomenons, which I think is something you wanted to avoid in this post.

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